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ORCIDJoël Ouaknine
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- affiliation: University of Oxford, Department of Computer Science, UK
- affiliation: Max Planck Institute for Software Systems, Saarbrücken, Germany
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2020 – today
- 2024
[j40]Engel Lefaucheux, Joël Ouaknine
, David Purser, James Worrell:
Porous invariants for linear systems. Formal Methods Syst. Des. 63(1): 235-271 (2024)- [c133]Quentin Guilmant, Joël Ouaknine:
Inaproximability in Weighted Timed Games. CONCUR 2024: 27:1-27:15 - [c132]Rajab Aghamov, Christel Baier, Toghrul Karimov, Joël Ouaknine, Jakob Piribauer:
Linear dynamical systems with continuous weight functions. HSCC 2024: 22:1-22:11 - [c131]Quentin Guilmant, Engel Lefaucheux, Joël Ouaknine, James Worrell:
The 2-Dimensional Constraint Loop Problem Is Decidable. ICALP 2024: 140:1-140:21 - [c130]Pavol Kebis, Florian Luca, Joël Ouaknine, Andrew Scoones, James Worrell:
On Transcendence of Numbers Related to Sturmian and Arnoux-Rauzy Words. ICALP 2024: 144:1-144:15 - [c129]Valérie Berthé, Toghrul Karimov, Joris Nieuwveld, Joël Ouaknine, Mihir Vahanwala, James Worrell:
On the Decidability of Monadic Second-Order Logic with Arithmetic Predicates. LICS 2024: 11:1-11:14 - [c128]Julian D'Costa, Joël Ouaknine, James Worrell:
Nonnegativity Problems for Matrix Semigroups. STACS 2024: 27:1-27:16 - [i64]Gorav Jindal, Joël Ouaknine:
On the Counting Complexity of the Skolem Problem. CoRR abs/2403.00098 (2024) - [i63]Toghrul Karimov, Edon Kelmendi, Joël Ouaknine, James Worrell:
Multiple Reachability in Linear Dynamical Systems. CoRR abs/2403.06515 (2024) - [i62]Pavol Kebis, Florian Luca, Joël Ouaknine, Andrew Scoones, James Worrell:
On Transcendence of Numbers Related to Sturmian and Arnoux-Rauzy Words. CoRR abs/2405.05279 (2024) - [i61]Valérie Berthé, Toghrul Karimov, Joris Nieuwveld, Joël Ouaknine, Mihir Vahanwala, James Worrell:
On the Decidability of Monadic Second-Order Logic with Arithmetic Predicates. CoRR abs/2405.07953 (2024) - [i60]Quentin Guilmant, Engel Lefaucheux, Joël Ouaknine, James Worrell:
The 2-Dimensional Constraint Loop Problem is Decidable. CoRR abs/2405.12992 (2024) - [i59]Rajab Aghamov, Christel Baier, Toghrul Karimov, Joris Nieuwveld, Joël Ouaknine, Jakob Piribauer, Mihir Vahanwala:
Model Checking Markov Chains as Distribution Transformers. CoRR abs/2406.15087 (2024) - [i58]Toghrul Karimov, Florian Luca, Joris Nieuwveld, Joël Ouaknine, James Worrell:
On the Decidability of Presburger Arithmetic Expanded with Powers. CoRR abs/2407.05191 (2024) - [i57]Toghrul Karimov, Joël Ouaknine, James Worrell:
Verification of Linear Dynamical Systems via O-Minimality of Real Numbers. CoRR abs/2410.13053 (2024) - 2023
- [j39]Ventsislav Chonev, Joël Ouaknine, James Worrell:
On the Zeros of Exponential Polynomials. J. ACM 70(4): 26:1-26:26 (2023) - [j38]Ehud Hrushovski, Joël Ouaknine, Amaury Pouly, James Worrell:
On Strongest Algebraic Program Invariants. J. ACM 70(5): 29:1-29:22 (2023) - [j37]Yuri Bilu, Florian Luca, Joris Nieuwveld, Joël Ouaknine, James Worrell:
On the 𝑝-adic zeros of the Tribonacci sequence. Math. Comput. 93(347): 1333-1353 (2023) - [c127]George Kenison, Joris Nieuwveld, Joël Ouaknine, James Worrell:
Positivity Problems for Reversible Linear Recurrence Sequences. ICALP 2023: 130:1-130:17 - [c126]Faraz Ghahremani, Edon Kelmendi, Joël Ouaknine:
Reachability in Injective Piecewise Affine Maps. LICS 2023: 1-11 - [c125]Toghrul Karimov, Edon Kelmendi, Joris Nieuwveld, Joël Ouaknine, James Worrell:
The Power of Positivity. LICS 2023: 1-11 - [c124]Engel Lefaucheux, Joël Ouaknine, David Purser, Mohammadamin Sharifi:
Model Checking Linear Dynamical Systems under Floating-point Rounding. TACAS (1) 2023: 47-65 - [i56]Faraz Ghahremani, Edon Kelmendi, Joël Ouaknine:
Reachability in Injective Piecewise Affine Maps. CoRR abs/2301.09752 (2023) - [i55]Florian Luca, James Maynard, Armand Noubissie, Joël Ouaknine, James Worrell:
Skolem Meets Bateman-Horn. CoRR abs/2308.01152 (2023) - [i54]Florian Luca, Joël Ouaknine, James Worrell:
Transcendence of Sturmian Numbers over an Algebraic Base. CoRR abs/2308.13657 (2023) - [i53]Valérie Berthé, Toghrul Karimov, Joël Ouaknine, Mihir Vahanwala, James Worrell:
The Monadic Theory of Toric Words. CoRR abs/2311.04895 (2023) - [i52]Julian D'Costa, Joël Ouaknine, James Worrell:
Nonnegativity Problems for Matrix Semigroups. CoRR abs/2311.06241 (2023) - 2022
- [j36]Dror Fried, Axel Legay, Joël Ouaknine, Moshe Y. Vardi:
Sequential Relational Decomposition. Log. Methods Comput. Sci. 18(1) (2022) - [j35]Toghrul Karimov, Engel Lefaucheux, Joël Ouaknine, David Purser, Anton Varonka, Markus A. Whiteland, James Worrell:
What's decidable about linear loops? Proc. ACM Program. Lang. 6(POPL): 1-25 (2022) - [j34]Shaull Almagor, Dmitry Chistikov, Joël Ouaknine, James Worrell:
O-Minimal Invariants for Discrete-Time Dynamical Systems. ACM Trans. Comput. Log. 23(2): 9:1-9:20 (2022) - [c123]Toghrul Karimov, Edon Kelmendi, Joël Ouaknine, James Worrell:
What's Decidable About Discrete Linear Dynamical Systems? Principles of Systems Design 2022: 21-38 - [c122]Christel Baier, Florian Funke, Simon Jantsch, Toghrul Karimov, Engel Lefaucheux, Joël Ouaknine, David Purser, Markus A. Whiteland, James Worrell:
Parameter Synthesis for Parametric Probabilistic Dynamical Systems and Prefix-Independent Specifications. CONCUR 2022: 10:1-10:16 - [c121]Florian Luca, Joël Ouaknine, James Worrell:
Algebraic Model Checking for Discrete Linear Dynamical Systems. FORMATS 2022: 3-15 - [c120]Richard Lipton, Florian Luca, Joris Nieuwveld, Joël Ouaknine, David Purser, James Worrell:
On the Skolem Problem and the Skolem Conjecture. LICS 2022: 5:1-5:9 - [c119]Yuri Bilu, Florian Luca, Joris Nieuwveld, Joël Ouaknine, David Purser, James Worrell:
Skolem Meets Schanuel. MFCS 2022: 20:1-20:15 - [c118]Julian D'Costa, Engel Lefaucheux, Eike Neumann, Joël Ouaknine, James Worrell:
Bounding the Escape Time of a Linear Dynamical System over a Compact Semialgebraic Set. MFCS 2022: 39:1-39:14 - [c117]Julian D'Costa, Toghrul Karimov, Rupak Majumdar, Joël Ouaknine, Mahmoud Salamati, James Worrell:
The Pseudo-Reachability Problem for Diagonalisable Linear Dynamical Systems. MFCS 2022: 40:1-40:13 - [c116]Florian Luca, Joël Ouaknine, James Worrell:
A Universal Skolem Set of Positive Lower Density. MFCS 2022: 73:1-73:12 - [i51]Julian D'Costa, Toghrul Karimov, Joël Ouaknine, Mahmoud Salamati, James Worrell:
The Pseudo-Reachability Problem for Diagonalisable Linear Dynamical Systems. CoRR abs/2204.12253 (2022) - [i50]Yuri Bilu, Florian Luca, Joris Nieuwveld, Joël Ouaknine, David Purser, James Worrell:
Skolem Meets Schanuel. CoRR abs/2204.13417 (2022) - [i49]Toghrul Karimov, Edon Kelmendi, Joël Ouaknine, James Worrell:
What's Decidable about Discrete Linear Dynamical Systems? CoRR abs/2206.11412 (2022) - [i48]Julian D'Costa, Engel Lefaucheux, Eike Neumann, Joël Ouaknine, James Worrell:
Bounding the Escape Time of a Linear Dynamical System over a Compact Semialgebraic Set. CoRR abs/2207.01550 (2022) - [i47]Engel Lefaucheux, Joël Ouaknine, David Purser, Mohammadamin Sharifi:
Model Checking Linear Dynamical Systems under Floating-point Rounding. CoRR abs/2211.04301 (2022) - 2021
- [j33]Mikolaj Bojanczyk, Thomas Brihaye, Christoph Haase, Slawomir Lasota, Joël Ouaknine, Igor Potapov:
Preface. Inf. Comput. 277: 104579 (2021) - [j32]Shaull Almagor, Joël Ouaknine, James Worrell:
First-Order Orbit Queries. Theory Comput. Syst. 65(4): 638-661 (2021) - [j31]Shaull Almagor, Toghrul Karimov, Edon Kelmendi, Joël Ouaknine, James Worrell:
Deciding ω-regular properties on linear recurrence sequences. Proc. ACM Program. Lang. 5(POPL): 1-24 (2021) - [c115]Engel Lefaucheux, Joël Ouaknine, David Purser, James Worrell:
Porous Invariants. CAV (2) 2021: 172-194 - [c114]Christel Baier, Florian Funke, Simon Jantsch, Toghrul Karimov, Engel Lefaucheux, Florian Luca, Joël Ouaknine, David Purser, Markus A. Whiteland, James Worrell:
The Orbit Problem for Parametric Linear Dynamical Systems. CONCUR 2021: 28:1-28:17 - [c113]Eike Neumann, Joël Ouaknine, James Worrell:
Decision Problems for Second-Order Holonomic Recurrences. ICALP 2021: 99:1-99:20 - [c112]Florian Luca, Joël Ouaknine, James Worrell:
Universal Skolem Sets. LICS 2021: 1-6 - [c111]Joël Ouaknine:
Holonomic Techniques, Periods, and Decision Problems (Invited Talk). MFCS 2021: 3:1-3:1 - [c110]Julian D'Costa, Engel Lefaucheux, Eike Neumann, Joël Ouaknine, James Worrell:
On the Complexity of the Escape Problem for Linear Dynamical Systems over Compact Semialgebraic Sets. MFCS 2021: 33:1-33:21 - [c109]Julian D'Costa, Toghrul Karimov, Rupak Majumdar, Joël Ouaknine, Mahmoud Salamati, Sadegh Soudjani, James Worrell:
The Pseudo-Skolem Problem is Decidable. MFCS 2021: 34:1-34:21 - [c108]George Kenison, Oleksiy Klurman, Engel Lefaucheux, Florian Luca, Pieter Moree, Joël Ouaknine, Markus A. Whiteland, James Worrell:
On Positivity and Minimality for Second-Order Holonomic Sequences. MFCS 2021: 67:1-67:15 - [i46]Christel Baier, Florian Funke, Simon Jantsch, Engel Lefaucheux, Florian Luca, Joël Ouaknine, David Purser, Markus A. Whiteland, James Worrell:
The Orbit Problem for Parametric Linear Dynamical Systems. CoRR abs/2104.10634 (2021) - [i45]Engel Lefaucheux, Joël Ouaknine, David Purser, James Worrell:
Porous Invariants. CoRR abs/2106.00662 (2021) - [i44]Julian D'Costa, Engel Lefaucheux, Eike Neumann, Joël Ouaknine, James Worrell:
On the Complexity of the Escape Problem for Linear Dynamical Systems over Compact Semialgebraic Sets. CoRR abs/2107.02060 (2021) - 2020
- [c107]Eike Neumann, Joël Ouaknine, James Worrell:
On Ranking Function Synthesis and Termination for Polynomial Programs. CONCUR 2020: 15:1-15:15 - [c106]Rupak Majumdar, Joël Ouaknine, Amaury Pouly, James Worrell:
Algebraic Invariants for Linear Hybrid Automata. CONCUR 2020: 32:1-32:17 - [c105]Joël Ouaknine:
Holonomic Techniques, Periods, and Decision Problems (Invited Talk). FSTTCS 2020: 4:1-4:3 - [c104]Christel Baier, Florian Funke, Simon Jantsch, Toghrul Karimov, Engel Lefaucheux, Joël Ouaknine, Amaury Pouly, David Purser, Markus A. Whiteland:
Reachability in Dynamical Systems with Rounding. FSTTCS 2020: 36:1-36:17 - [c103]Shaull Almagor, Edon Kelmendi, Joël Ouaknine, James Worrell:
Invariants for Continuous Linear Dynamical Systems. ICALP 2020: 107:1-107:15 - [c102]George Kenison, Richard Lipton, Joël Ouaknine, James Worrell:
On the skolem problem and prime powers. ISSAC 2020: 289-296 - [c101]Toghrul Karimov, Joël Ouaknine, James Worrell:
On LTL Model Checking for Low-Dimensional Discrete Linear Dynamical Systems. MFCS 2020: 54:1-54:14 - [c100]Julian D'Costa, Engel Lefaucheux, Joël Ouaknine, James Worrell:
How Fast Can You Escape a Compact Polytope? STACS 2020: 49:1-49:11 - [i43]Shaull Almagor, Edon Kelmendi, Joël Ouaknine, James Worrell:
Invariants for Continuous Linear Dynamical Systems. CoRR abs/2004.11661 (2020) - [i42]George Kenison, Richard Lipton, Joël Ouaknine, James Worrell:
On the Skolem Problem and Prime Powers. CoRR abs/2006.07432 (2020) - [i41]Toghrul Karimov, Joël Ouaknine, James Worrell:
On LTL Model Checking for Low-Dimensional Discrete Linear Dynamical Systems. CoRR abs/2007.02911 (2020) - [i40]George Kenison, Oleksiy Klurman, Engel Lefaucheux, Florian Luca, Pieter Moree, Joël Ouaknine, Markus A. Whiteland, James Worrell:
On Positivity and Minimality for Second-Order Holonomic Sequences. CoRR abs/2007.12282 (2020) - [i39]Christel Baier, Florian Funke, Simon Jantsch, Toghrul Karimov, Engel Lefaucheux, Joël Ouaknine, Amaury Pouly, David Purser, Markus A. Whiteland:
Reachability in Dynamical Systems with Rounding. CoRR abs/2009.13353 (2020) - [i38]Shaull Almagor, Toghrul Karimov, Edon Kelmendi, Joël Ouaknine, James Worrell:
Deciding ω-Regular Properties on Linear Recurrence Sequences. CoRR abs/2010.14432 (2020)
2010 – 2019
- 2019
- [j30]Joël Ouaknine, Amaury Pouly, João Sousa Pinto, James Worrell:
On the Decidability of Membership in Matrix-exponential Semigroups. J. ACM 66(3): 15:1-15:24 (2019) - [j29]Nir Drucker, Hsi-Ming Ho, Joël Ouaknine, Michal Penn, Ofer Strichman:
Cyclic-routing of Unmanned Aerial Vehicles. J. Comput. Syst. Sci. 103: 18-45 (2019) - [j28]Hsi-Ming Ho, Joël Ouaknine, James Worrell:
On the Expressiveness and Monitoring of Metric Temporal Logic. Log. Methods Comput. Sci. 15(2) (2019) - [j27]Nathanaël Fijalkow, Pierre Ohlmann, Joël Ouaknine, Amaury Pouly, James Worrell:
Complete Semialgebraic Invariant Synthesis for the Kannan-Lipton Orbit Problem. Theory Comput. Syst. 63(5): 1027-1048 (2019) - [c99]Joël Ouaknine:
Program Invariants (Invited Talk). CONCUR 2019: 3:1-3:1 - [c98]Nathanaël Fijalkow, Joël Ouaknine, Amaury Pouly, João Sousa Pinto, James Worrell:
On the decidability of reachability in linear time-invariant systems. HSCC 2019: 77-86 - [c97]Thomas Colcombet, Joël Ouaknine, Pavel Semukhin, James Worrell:
On Reachability Problems for Low-Dimensional Matrix Semigroups. ICALP 2019: 44:1-44:15 - [c96]Mehran Hosseini, Joël Ouaknine, James Worrell:
Termination of Linear Loops over the Integers. ICALP 2019: 118:1-118:13 - [c95]Nathanaël Fijalkow, Engel Lefaucheux, Pierre Ohlmann, Joël Ouaknine, Amaury Pouly, James Worrell:
On the Monniaux Problem in Abstract Interpretation. SAS 2019: 162-180 - [c94]Shaull Almagor, Joël Ouaknine, James Worrell:
The Semialgebraic Orbit Problem. STACS 2019: 6:1-6:15 - [i37]Shaull Almagor, Joël Ouaknine, James Worrell:
The Semialgebraic Orbit Problem. CoRR abs/1901.11023 (2019) - [i36]Mehran Hosseini, Joël Ouaknine, James Worrell:
On Termination of Integer Linear Loops. CoRR abs/1902.07465 (2019) - [i35]Thomas Colcombet, Joël Ouaknine, Pavel Semukhin, James Worrell:
On reachability problems for low dimensional matrix semigroups. CoRR abs/1902.09597 (2019) - [i34]Rupak Majumdar, Joël Ouaknine, Amaury Pouly, James Worrell:
Algebraic Invariants for Linear Hybrid Automata. CoRR abs/1902.10452 (2019) - [i33]Dror Fried, Axel Legay, Joël Ouaknine, Moshe Y. Vardi:
Sequential Relational Decomposition. CoRR abs/1903.01368 (2019) - [i32]Nathanaël Fijalkow, Engel Lefaucheux, Pierre Ohlmann, Joël Ouaknine, Amaury Pouly, James Worrell:
On the Monniaux Problem in Abstract Interpretation. CoRR abs/1907.08257 (2019) - 2018
- [j26]Antonia Lechner, Richard Mayr, Joël Ouaknine, Amaury Pouly, James Worrell:
Model Checking Flat Freeze LTL on One-Counter Automata. Log. Methods Comput. Sci. 14(4) (2018) - [j25]Joël Ouaknine, Igor Potapov, James Worrell:
Reachability Problems 2014: Special issue. Theor. Comput. Sci. 735: 1 (2018) - [c93]Shaull Almagor, Brynmor Chapman, Mehran Hosseini, Joël Ouaknine, James Worrell:
Effective Divergence Analysis for Linear Recurrence Sequences. CONCUR 2018: 42:1-42:15 - [c92]Shaull Almagor, Dmitry Chistikov, Joël Ouaknine, James Worrell:
O-Minimal Invariants for Linear Loops. ICALP 2018: 114:1-114:14 - [c91]Gerco van Heerdt, Justin Hsu, Joël Ouaknine, Alexandra Silva:
Convex Language Semantics for Nondeterministic Probabilistic Automata. ICTAC 2018: 472-492 - [c90]Dror Fried, Axel Legay, Joël Ouaknine, Moshe Y. Vardi:
Sequential Relational Decomposition. LICS 2018: 432-441 - [c89]Ehud Hrushovski, Joël Ouaknine, Amaury Pouly, James Worrell:
Polynomial Invariants for Affine Programs. LICS 2018: 530-539 - [p3]Patricia Bouyer, Uli Fahrenberg, Kim Guldstrand Larsen, Nicolas Markey, Joël Ouaknine, James Worrell:
Model Checking Real-Time Systems. Handbook of Model Checking 2018: 1001-1046 - [i31]Ehud Hrushovski, Joël Ouaknine, Amaury Pouly, James Worrell:
Polynomial Invariants for Affine Programs. CoRR abs/1802.01810 (2018) - [i30]Nathanaël Fijalkow, Joël Ouaknine, Amaury Pouly, João Sousa Pinto, James Worrell:
On the Decidability of Reachability in Linear Time-Invariant Systems. CoRR abs/1802.06575 (2018) - [i29]Shaull Almagor, Dmitry Chistikov, Joël Ouaknine, James Worrell:
O-Minimal Invariants for Linear Loops. CoRR abs/1802.09263 (2018) - [i28]Hsi-Ming Ho, Joël Ouaknine, James Worrell:
On the Expressiveness and Monitoring of Metric Temporal Logic. CoRR abs/1803.02653 (2018) - [i27]Gerco van Heerdt, Justin Hsu, Joël Ouaknine, Alexandra Silva:
Convex Language Semantics for Nondeterministic Probabilistic Automata. CoRR abs/1805.11550 (2018) - [i26]Shaull Almagor, Brynmor Chapman, Mehran Hosseini, Joël Ouaknine, James Worrell:
Effective Divergence Analysis for Linear Recurrence Sequences. CoRR abs/1806.07740 (2018) - 2017
- [j24]Daniel Bundala, Joël Ouaknine:
On parametric timed automata and one-counter machines. Inf. Comput. 253: 272-303 (2017) - [c88]Patricia Bouyer, François Laroussinie, Nicolas Markey, Joël Ouaknine, James Worrell:
Timed Temporal Logics. Models, Algorithms, Logics and Tools 2017: 211-230 - [c87]Joël Ouaknine, João Sousa Pinto, James Worrell:
On the Polytope Escape Problem for Continuous Linear Dynamical Systems. HSCC 2017: 11-17 - [c86]Shaull Almagor, Joël Ouaknine, James Worrell:
The Polytope-Collision Problem. ICALP 2017: 24:1-24:14 - [c85]Joël Ouaknine:
LICS 2017 foreword. LICS 2017: ii-iv - [c84]Nathanaël Fijalkow, Pierre Ohlmann, Joël Ouaknine, Amaury Pouly, James Worrell:
Semialgebraic Invariant Synthesis for the Kannan-Lipton Orbit Problem. STACS 2017: 29:1-29:13 - [i25]Nathanaël Fijalkow, Pierre Ohlmann, Joël Ouaknine, Amaury Pouly, James Worrell:
Semialgebraic Invariant Synthesis for the Kannan-Lipton Orbit Problem. CoRR abs/1701.02162 (2017) - 2016
- [j23]Christoph Haase, Joël Ouaknine, James Worrell:
Relating Reachability Problems in Timed and Counter Automata. Fundam. Informaticae 143(3-4): 317-338 (2016) - [j22]Ventsislav Chonev, Joël Ouaknine, James Worrell:
On the Complexity of the Orbit Problem. J. ACM 63(3): 23:1-23:18 (2016) - [j21]Ranko Lazic, Joël Ouaknine, James Worrell:
Zeno, Hercules, and the Hydra: Safety Metric Temporal Logic is Ackermann-Complete. ACM Trans. Comput. Log. 17(3): 16 (2016) - [c83]Antonia Lechner, Richard Mayr, Joël Ouaknine, Amaury Pouly, James Worrell:
Model Checking Flat Freeze LTL on One-Counter Automata. CONCUR 2016: 29:1-29:14 - [c82]Ventsislav Chonev, Joël Ouaknine, James Worrell:
On the Skolem Problem for Continuous Linear Dynamical Systems. ICALP 2016: 100:1-100:13 - [c81]Maria Bruna, Radu Grigore, Stefan Kiefer, Joël Ouaknine, James Worrell:
Proving the Herman-Protocol Conjecture. ICALP 2016: 104:1-104:12 - [c80]Ventsislav Chonev, Joël Ouaknine, James Worrell:
On Recurrent Reachability for Continuous Linear Dynamical Systems. LICS 2016: 515-524 - [c79]Joël Ouaknine, Amaury Pouly, João Sousa Pinto, James Worrell:
Solvability of Matrix-Exponential Equations. LICS 2016: 798-806 - [i24]Joël Ouaknine, Amaury Pouly, João Sousa Pinto, James Worrell:
Solvability of Matrix-Exponential Equations. CoRR abs/1601.05002 (2016) - [i23]Antonia Lechner, Richard Mayr, Joël Ouaknine, Amaury Pouly, James Worrell:
Model Checking Flat Freeze LTL on One-Counter Automata. CoRR abs/1606.02643 (2016) - [i22]Shaull Almagor, Joël Ouaknine, James Worrell:
The Polytope-Collision Problem. CoRR abs/1611.01344 (2016) - 2015
- [j20]S. Akshay, Timos Antonopoulos, Joël Ouaknine, James Worrell:
Reachability problems for Markov chains. Inf. Process. Lett. 115(2): 155-158 (2015) - [j19]Joël Ouaknine, James Worrell:
On linear recurrence sequences and loop termination. ACM SIGLOG News 2(2): 4-13 (2015) - [c78]Hsi-Ming Ho, Joël Ouaknine:
The Cyclic-Routing UAV Problem is PSPACE-Complete. FoSSaCS 2015: 328-342 - [c77]Antonia Lechner, Joël Ouaknine, James Worrell:
On the Complexity of Linear Arithmetic with Divisibility. LICS 2015: 667-676 - [c76]Ventsislav Chonev, Joël Ouaknine, James Worrell:
The Polyhedron-Hitting Problem. SODA 2015: 940-956 - [c75]Joël Ouaknine, João Sousa Pinto, James Worrell:
On Termination of Integer Linear Loops. SODA 2015: 957-969 - [c74]Esther Galby, Joël Ouaknine, James Worrell:
On Matrix Powering in Low Dimensions. STACS 2015: 329-340 - [i21]Maria Bruna, Radu Grigore, Stefan Kiefer, Joël Ouaknine, James Worrell:
Proving the Herman-Protocol Conjecture. CoRR abs/1504.01130 (2015) - [i20]Ventsislav Chonev, Joël Ouaknine, James Worrell:
On the Decidability of the Bounded Continuous Skolem Problem. CoRR abs/1506.00695 (2015) - [i19]Joël Ouaknine, João Sousa Pinto, James Worrell:
The Polyhedral Escape Problem is Decidable. CoRR abs/1507.03166 (2015) - [i18]Ventsislav Chonev, Joël Ouaknine, James Worrell:
On the Decidability of the Continuous Infinite Zeros Problem. CoRR abs/1507.03632 (2015) - 2014
- [c73]Timos Antonopoulos, Nikos Gorogiannis, Christoph Haase, Max I. Kanovich, Joël Ouaknine:
Foundations for Decision Problems in Separation Logic with General Inductive Predicates. FoSSaCS 2014: 411-425 - [c72]Daniel Bundala, Joël Ouaknine:
On the Complexity of Temporal-Logic Path Checking. ICALP (2) 2014: 86-97 - [c71]Joël Ouaknine, James Worrell:
On the Positivity Problem for Simple Linear Recurrence Sequences, . ICALP (2) 2014: 318-329 - [c70]Joël Ouaknine, James Worrell:
Ultimate Positivity is Decidable for Simple Linear Recurrence Sequences. ICALP (2) 2014: 330-341 - [c69]Daniel Bundala, Joël Ouaknine:
Advances in Parametric Real-Time Reasoning. MFCS (1) 2014: 123-134 - [c68]Hsi-Ming Ho, Joël Ouaknine, James Worrell:
Online Monitoring of Metric Temporal Logic. RV 2014: 178-192 - [c67]Joël Ouaknine, James Worrell:
Positivity Problems for Low-Order Linear Recurrence Sequences. SODA 2014: 366-379 - [p2]Philip J. Armstrong, Gavin Lowe, Joël Ouaknine, Bill Roscoe:
Model checking Timed CSP. HOWARD-60 2014: 13-33 - [e3]Joël Ouaknine, Igor Potapov, James Worrell:
Reachability Problems - 8th International Workshop, RP 2014, Oxford, UK, September 22-24, 2014. Proceedings. Lecture Notes in Computer Science 8762, Springer 2014, ISBN 978-3-319-11438-5 [contents] - [i17]Ventsislav Chonev, Joël Ouaknine, James Worrell:
The Polyhedron-Hitting Problem. CoRR abs/1407.1889 (2014) - [i16]Joël Ouaknine, João Sousa Pinto, James Worrell:
On Termination of Integer Linear Loops. CoRR abs/1407.1891 (2014) - [i15]Hsi-Ming Ho, Joël Ouaknine:
The CR-UAV Problem is PSPACE-Complete. CoRR abs/1411.2874 (2014) - [i14]Javier Esparza, Alain Finkel, Pierre McKenzie, Joël Ouaknine:
Reachability Problems for Infinite-State Systems (Dagstuhl Seminar 14141). Dagstuhl Reports 4(3): 153-180 (2014) - 2013
- [j18]Stefan Kiefer, Andrzej S. Murawski, Joël Ouaknine, Björn Wachter, James Worrell:
On the Complexity of Equivalence and Minimisation for Q-weighted Automata. Log. Methods Comput. Sci. 9(1) (2013) - [j17]Joël Ouaknine, Hristina Palikareva, A. W. Roscoe, James Worrell:
A Static Analysis Framework for Livelock Freedom in CSP. Log. Methods Comput. Sci. 9(3) (2013) - [j16]Stefan Kiefer, Andrzej S. Murawski, Joël Ouaknine, Björn Wachter, James Worrell:
Algorithmic probabilistic game semantics - Playing games with automata. Formal Methods Syst. Des. 43(2): 285-312 (2013) - [c66]Thomas Brihaye, Laurent Doyen, Gilles Geeraerts, Joël Ouaknine, Jean-François Raskin, James Worrell:
Time-Bounded Reachability for Monotonic Hybrid Automata: Complexity and Fixed Points. ATVA 2013: 55-70 - [c65]Christoph Haase, Samin Ishtiaq, Joël Ouaknine, Matthew J. Parkinson:
SeLoger: A Tool for Graph-Based Reasoning in Separation Logic. CAV 2013: 790-795 - [c64]Joël Ouaknine:
Decision Problems for Linear Recurrence Sequences. FCT 2013: 2 - [c63]Björn Wachter, Daniel Kroening, Joël Ouaknine:
Verifying multi-threaded software with impact. FMCAD 2013: 210-217 - [c62]Joël Ouaknine:
Specification and Verification of Linear Dynamical Systems: Advances and Challenges. FroCos 2013: 197 - [c61]Joël Ouaknine:
Discrete Linear Dynamical Systems. LATA 2013: 42 - [c60]Paul Hunter, Joël Ouaknine, James Worrell:
Expressive Completeness for Metric Temporal Logic. LICS 2013: 349-357 - [c59]Ranko Lazic, Joël Ouaknine, James Worrell:
Zeno, Hercules and the Hydra: Downward Rational Termination Is Ackermannian. MFCS 2013: 643-654 - [c58]Ventsislav Chonev, Joël Ouaknine, James Worrell:
The orbit problem in higher dimensions. STOC 2013: 941-950 - [c57]Joël Ouaknine:
Decision Problems for Linear Recurrence Sequences. SCSS 2013: 3 - [i13]Ventsislav Chonev, Joël Ouaknine, James Worrell:
The Orbit Problem in Higher Dimensions. CoRR abs/1303.2981 (2013) - [i12]Joël Ouaknine, James Worrell:
Positivity Problems for Low-Order Linear Recurrence Sequences. CoRR abs/1307.2779 (2013) - [i11]Joël Ouaknine, James Worrell:
Effective Positivity Problems for Simple Linear Recurrence Sequences. CoRR abs/1309.1550 (2013) - [i10]Joël Ouaknine, James Worrell:
Ultimate Positivity is Decidable for Simple Linear Recurrence Sequences. CoRR abs/1309.1914 (2013) - [i9]Daniel Bundala, Joël Ouaknine:
On the Complexity of Path Checking of Temporal Logics. CoRR abs/1312.7603 (2013) - 2012
- [j15]Patricia Bouyer, Nicolas Markey, Joël Ouaknine, Philippe Schnoebelen, James Worrell:
On termination and invariance for faulty channel machines. Formal Aspects Comput. 24(4-6): 595-607 (2012) - [j14]Stefan Kiefer, Andrzej S. Murawski, Joël Ouaknine, Björn Wachter, James Worrell:
Three tokens in Herman's algorithm. Formal Aspects Comput. 24(4-6): 671-678 (2012) - [j13]Hristina Palikareva, Joël Ouaknine, A. W. Roscoe:
SAT-solving in CSP trace refinement. Sci. Comput. Program. 77(10-11): 1178-1197 (2012) - [c56]Stefan Kiefer, Andrzej S. Murawski, Joël Ouaknine, Björn Wachter, James Worrell:
APEX: An Analyzer for Open Probabilistic Programs. CAV 2012: 693-698 - [c55]Philip J. Armstrong, Michael Goldsmith, Gavin Lowe, Joël Ouaknine, Hristina Palikareva, A. W. Roscoe, James Worrell:
Recent Developments in FDR. CAV 2012: 699-704 - [c54]Stefan Göller, Christoph Haase, Joël Ouaknine, James Worrell:
Branching-Time Model Checking of Parametric One-Counter Automata. FoSSaCS 2012: 406-420 - [c53]Stefan Kiefer, Andrzej S. Murawski, Joël Ouaknine, Björn Wachter, James Worrell:
On the Complexity of the Equivalence Problem for Probabilistic Automata. FoSSaCS 2012: 467-481 - [c52]Daniel Bundala, Joël Ouaknine, James Worrell:
On the Magnitude of Completeness Thresholds in Bounded Model Checking. LICS 2012: 155-164 - [c51]Joël Ouaknine, James Worrell:
Decision Problems for Linear Recurrence Sequences. RP 2012: 21-28 - [c50]Christoph Haase, Joël Ouaknine, James Worrell:
On the Relationship between Reachability Problems in Timed and Counter Automata. RP 2012: 54-65 - [i8]Paul Hunter, Joël Ouaknine, James Worrell:
Expressive Completeness of Metric Temporal Logic. CoRR abs/1208.4993 (2012) - [i7]Paul Hunter, Joël Ouaknine, James Worrell:
When is Metric Temporal Logic Expressively Complete? CoRR abs/1209.0516 (2012) - [i6]Thomas Brihaye, Laurent Doyen, Gilles Geeraerts, Joël Ouaknine, Jean-François Raskin, James Worrell:
Time-bounded Reachability for Hybrid Automata: Complexity and Fixpoints. CoRR abs/1211.1276 (2012) - 2011
- [c49]Stefan Kiefer, Andrzej S. Murawski, Joël Ouaknine, Björn Wachter, James Worrell:
Language Equivalence for Probabilistic Automata. CAV 2011: 526-540 - [c48]Daniel Kroening, Joël Ouaknine, Ofer Strichman, Thomas Wahl, James Worrell:
Linear Completeness Thresholds for Bounded Model Checking. CAV 2011: 557-572 - [c47]Byron Cook, Christoph Haase, Joël Ouaknine, Matthew J. Parkinson, James Worrell:
Tractable Reasoning in a Fragment of Separation Logic. CONCUR 2011: 235-249 - [c46]Joël Ouaknine, Hristina Palikareva, A. W. Roscoe, James Worrell:
Static Livelock Analysis in CSP. CONCUR 2011: 389-403 - [c45]Mark Jenkins, Joël Ouaknine, Alexander Rabinovich, James Worrell:
The Church Synthesis Problem with Metric. CSL 2011: 307-321 - [c44]Thomas Brihaye, Laurent Doyen, Gilles Geeraerts, Joël Ouaknine, Jean-François Raskin, James Worrell:
On Reachability for Hybrid Automata over Bounded Time. ICALP (2) 2011: 416-427 - [c43]Stefan Kiefer, Andrzej S. Murawski, Joël Ouaknine, James Worrell, Lijun Zhang:
On Stabilization in Herman's Algorithm. ICALP (2) 2011: 466-477 - [c42]Felix Arends, Joël Ouaknine, Charles W. Wampler:
On Searching for Small Kochen-Specker Vector Systems. WG 2011: 23-34 - [c41]Michael W. Mislove, Joël Ouaknine:
Preface. MFPS 2011: 1-3 - [e2]Michael W. Mislove, Joël Ouaknine:
Twenty-seventh Conference on the Mathematical Foundations of Programming Semantics, MFPS 2011, Pittsburgh, PA, USA, May 25-28, 2011. Electronic Notes in Theoretical Computer Science 276, Elsevier 2011 [contents] - [i5]Stefan Kiefer, Andrzej S. Murawski, Joël Ouaknine, James Worrell, Lijun Zhang:
On Stabilization in Herman's Algorithm. CoRR abs/1104.3100 (2011) - [i4]Thomas Brihaye, Laurent Doyen, Gilles Geeraerts, Joël Ouaknine, Jean-François Raskin, James Worrell:
On Reachability for Hybrid Automata over Bounded Time. CoRR abs/1104.5335 (2011) - [i3]Stefan Kiefer, Andrzej S. Murawski, Joël Ouaknine, Björn Wachter, James Worrell:
On the Complexity of the Equivalence Problem for Probabilistic Automata. CoRR abs/1112.4644 (2011) - 2010
- [c40]Paul Hunter, Patricia Bouyer, Nicolas Markey, Joël Ouaknine, James Worrell:
Computing Rational Radical Sums in Uniform TC^0. FSTTCS 2010: 308-316 - [c39]Joël Ouaknine, James Worrell:
Towards a Theory of Time-Bounded Verification. ICALP (2) 2010: 22-37 - [c38]Stefan Göller, Christoph Haase, Joël Ouaknine, James Worrell:
Model Checking Succinct and Parametric One-Counter Automata. ICALP (2) 2010: 575-586 - [c37]Mark Jenkins, Joël Ouaknine, Alexander Rabinovich, James Worrell:
Alternating Timed Automata over Bounded Time. LICS 2010: 60-69 - [p1]Christoph Haase, Joël Ouaknine, James Worrell:
On Process-Algebraic Extensions of Metric Temporal Logic. Reflections on the Work of C. A. R. Hoare 2010: 283-300
2000 – 2009
- 2009
- [j12]Hristina Palikareva, Joël Ouaknine, Bill Roscoe:
Faster FDR Counterexample Generation Using SAT-Solving. Electron. Commun. Eur. Assoc. Softw. Sci. Technol. 23 (2009) - [j11]Randal E. Bryant, Daniel Kroening, Joël Ouaknine, Sanjit A. Seshia, Ofer Strichman, Bryan A. Brady:
An abstraction-based decision procedure for bit-vector arithmetic. Int. J. Softw. Tools Technol. Transf. 11(2): 95-104 (2009) - [c36]Christoph Haase, Stephan Kreutzer, Joël Ouaknine, James Worrell:
Reachability in Succinct and Parametric One-Counter Automata. CONCUR 2009: 369-383 - [c35]Joël Ouaknine, Alexander Rabinovich, James Worrell:
Time-Bounded Verification. CONCUR 2009: 496-510 - [e1]Joël Ouaknine, Frits W. Vaandrager:
Formal Modeling and Analysis of Timed Systems, 7th International Conference, FORMATS 2009, Budapest, Hungary, September 14-16, 2009. Proceedings. Lecture Notes in Computer Science 5813, Springer 2009, ISBN 978-3-642-04367-3 [contents] - 2008
- [j10]Ranko Lazic, Thomas Christopher Newcomb, Joël Ouaknine, A. W. Roscoe, James Worrell:
Nets with Tokens which Carry Data. Fundam. Informaticae 88(3): 251-274 (2008) - [j9]Parosh Aziz Abdulla, Johann Deneux, Joël Ouaknine, Karin Quaas, James Worrell:
Universality Analysis for One-Clock Timed Automata. Fundam. Informaticae 89(4): 419-450 (2008) - [c34]Joël Ouaknine, James Worrell:
Some Recent Results in Metric Temporal Logic. FORMATS 2008: 1-13 - [c33]Patricia Bouyer, Nicolas Markey, Joël Ouaknine, James Worrell:
On Expressiveness and Complexity in Real-Time Model Checking. ICALP (2) 2008: 124-135 - [c32]Patricia Bouyer, Nicolas Markey, Joël Ouaknine, Philippe Schnoebelen, James Worrell:
On Termination for Faulty Channel Machines. STACS 2008: 121-132 - [c31]Axel Legay, Andrzej S. Murawski, Joël Ouaknine, James Worrell:
On Automated Verification of Probabilistic Programs. TACAS 2008: 173-187 - [i2]Patricia Bouyer, Nicolas Markey, Joël Ouaknine, Philippe Schnoebelen, James Worrell:
On Termination for Faulty Channel Machines. CoRR abs/0802.2839 (2008) - 2007
- [j8]Joël Ouaknine, James Worrell:
On the decidability and complexity of Metric Temporal Logic over finite words. Log. Methods Comput. Sci. 3(1) (2007) - [c30]Ranko Lazic, Thomas Christopher Newcomb, Joël Ouaknine, A. W. Roscoe, James Worrell:
Nets with Tokens Which Carry Data. ICATPN 2007: 301-320 - [c29]Sara Adams, Joël Ouaknine, James Worrell:
Undecidability of Universality for Timed Automata with Minimal Resources. FORMATS 2007: 25-37 - [c28]Parosh Aziz Abdulla, Joël Ouaknine, Karin Quaas, James Worrell:
Zone-Based Universality Analysis for Single-Clock Timed Automata. FSEN 2007: 98-112 - [c27]Patricia Bouyer, Nicolas Markey, Joël Ouaknine, James Worrell:
The Cost of Punctuality. LICS 2007: 109-120 - [c26]Randal E. Bryant, Daniel Kroening, Joël Ouaknine, Sanjit A. Seshia, Ofer Strichman, Bryan A. Brady:
Deciding Bit-Vector Arithmetic with Abstraction. TACAS 2007: 358-372 - [i1]Joël Ouaknine, James Worrell:
On the decidability and complexity of Metric Temporal Logic over finite words. CoRR abs/cs/0702120 (2007) - 2006
- [c25]Joël Ouaknine, James Worrell:
On Metric Temporal Logic and Faulty Turing Machines. FoSSaCS 2006: 217-230 - [c24]Inês Lynce, Joël Ouaknine:
Sudoku as a SAT Problem. AI&M 2006 - [c23]Joël Ouaknine, James Worrell:
Safety Metric Temporal Logic Is Fully Decidable. TACAS 2006: 411-425 - 2005
- [j7]Sagar Chaki, Edmund M. Clarke, Joël Ouaknine, Natasha Sharygina, Nishant Sinha:
Concurrent software verification with states, events, and deadlocks. Formal Aspects Comput. 17(4): 461-483 (2005) - [j6]Edmund M. Clarke, Daniel Kroening, Joël Ouaknine, Ofer Strichman:
Computational challenges in bounded model checking. Int. J. Softw. Tools Technol. Transf. 7(2): 174-183 (2005) - [j5]Joël Ouaknine:
Verification of Reactive Systems: Formal Methods and Algorithms. By Klaus Schneider. Springer, Texts in Theoretical Computer Science Series, 2004, ISBN: 3-540-00296-0, pp 600. Softw. Test. Verification Reliab. 15(3): 202-203 (2005) - [j4]Franck van Breugel, Michael W. Mislove, Joël Ouaknine, James Worrell:
Domain theory, testing and simulation for labelled Markov processes. Theor. Comput. Sci. 333(1-2): 171-197 (2005) - [c22]Andrzej S. Murawski, Joël Ouaknine:
On Probabilistic Program Equivalence and Refinement. CONCUR 2005: 156-170 - [c21]Parosh Aziz Abdulla, Johann Deneux, Joël Ouaknine, James Worrell:
Decidability and Complexity Results for Timed Automata via Channel Machines. ICALP 2005: 1089-1101 - [c20]Sagar Chaki, Edmund M. Clarke, Orna Grumberg, Joël Ouaknine, Natasha Sharygina, Tayssir Touili, Helmut Veith:
State/Event Software Verification for Branching-Time Specifications. IFM 2005: 53-69 - [c19]Joël Ouaknine, James Worrell:
On the Decidability of Metric Temporal Logic. LICS 2005: 188-197 - [c18]Murray Stokely, Sagar Chaki, Joël Ouaknine:
Parallel Assignments in Software Model Checking. SVV@ICFEM 2005: 77-94 - [c17]Joël Ouaknine, Steve A. Schneider:
Timed CSP: A Retrospective. APC 25 2005: 273-276 - [c16]Gavin Lowe, Joël Ouaknine:
On Timed Models and Full Abstraction. MFPS 2005: 497-519 - 2004
- [j3]Sagar Chaki, Edmund M. Clarke, Alex Groce, Joël Ouaknine, Ofer Strichman, Karen Yorav:
Efficient Verification of Sequential and Concurrent C Programs. Formal Methods Syst. Des. 25(2-3): 129-166 (2004) - [c15]Daniel Kroening, Joël Ouaknine, Sanjit A. Seshia, Ofer Strichman:
Abstraction-Based Satisfiability Solving of Presburger Arithmetic. CAV 2004: 308-320 - [c14]Michael W. Mislove, Joël Ouaknine, Dusko Pavlovic, James Worrell:
Duality for Labelled Markov Processes. FoSSaCS 2004: 393-407 - [c13]Sagar Chaki, Edmund M. Clarke, Joël Ouaknine, Natasha Sharygina, Nishant Sinha:
State/Event-Based Software Model Checking. IFM 2004: 128-147 - [c12]Joël Ouaknine, James Worrell:
On the Language Inclusion Problem for Timed Automata: Closing a Decidability Gap. LICS 2004: 54-63 - [c11]Sagar Chaki, Edmund M. Clarke, Joël Ouaknine, Natasha Sharygina:
Automated, compositional and iterative deadlock detection. MEMOCODE 2004: 201-210 - [c10]Edmund M. Clarke, Daniel Kroening, Joël Ouaknine, Ofer Strichman:
Completeness and Complexity of Bounded Model Checking. VMCAI 2004: 85-96 - 2003
- [j2]Edmund M. Clarke, Ansgar Fehnker, Zhi Han, Bruce H. Krogh, Joël Ouaknine, Olaf Stursberg, Michael Theobald:
Abstraction and Counterexample-Guided Refinement in Model Checking of Hybrid Systems. Int. J. Found. Comput. Sci. 14(4): 583-604 (2003) - [j1]Joël Ouaknine, James Worrell:
Timed CSP = Closed Timed epsilon-automata. Nord. J. Comput. 10(2): 99-133 (2003) - [c9]Franck van Breugel, Michael W. Mislove, Joël Ouaknine, James Worrell:
An Intrinsic Characterization of Approximate Probabilistic Bisimilarity. FoSSaCS 2003: 200-215 - [c8]Joël Ouaknine, James Worrell:
Universality and Language Inclusion for Open and Closed Timed Automata. HSCC 2003: 375-388 - [c7]Joël Ouaknine, James Worrell:
Revisiting Digitization, Robustness, and Decidability for Timed Automata. LICS 2003: 198-207 - [c6]Michael W. Mislove, Joël Ouaknine, James Worrell:
Axioms for Probability and Nondeterminism. EXPRESS 2003: 7-28 - [c5]Sagar Chaki, Joël Ouaknine, Karen Yorav, Edmund M. Clarke:
Automated Compositional Abstraction Refinement for Concurrent C Programs: A Two-Level Approach. SoftMC@CAV 2003: 417-432 - 2002
- [c4]Joël Ouaknine:
Digitisation and Full Abstraction for Dense-Time Model Checking. TACAS 2002: 37-51 - [c3]Keye Martin, Joël Ouaknine:
Informatic vs. Classical Differentiation on the Real Line. Workshop on Domains 2002: 133-140 - [c2]Joël Ouaknine, James Worrell:
Timed CSP = Closed Timed Safety Automata. EXPRESS 2002: 142-159 - 2000
- [b1]Joël Ouaknine:
Discrete analysis of continuous behaviour in real-time concurrent systems. University of Oxford, UK, 2000
1990 – 1999
- 1999
- [c1]Joël Ouaknine, George M. Reed:
Model-Checking Temporal Behaviour in CSP. PDPTA 1999: 295-304
Coauthor Index
[j40] [c131] [c130] [c129] [c128] [i63] [i62] [i61] [i60] [i58] [i57] [j39] [j38] [j37] [c127] [c125] [i55] [i54] [i53] [i52] [j35] [j34] [c123] [c122] [c121] [c120] [c119] [c118] [c117] [c116] [i51] [i50] [i49] [i48] [j32] [j31] [c115] [c114] [c113] [c112] [c110] [c109] [c108] [i46] [i45] [i44] [c107] [c106] [c103] [c102] [c101] [c100] [i43] [i42] [i41] [i40] [i38] [j30] [j28] [j27] [c98] [c97] [c96] [c95] [c94] [i37] [i36] [i35] [i34] [i32] [j26] [j25] [c93] [c92] [c89] [p3] [i31] [i30] [i29] [i28] [i26] [c88] [c87] [c86] [c84] [i25] [j23] [j22] [j21] [c83] [c82] [c81] [c80] [c79] [i24] [i23] [i22] [j20] [j19] [c77] [c76] [c75] [c74] [i21] [i20] [i19] [i18] [c71] [c70] [c68] [c67] [e3] [i17] [i16] [j18] [j17] [j16] [c66] [c60] [c59] [c58] [i13] [i12] [i11] [i10] [j15] [j14] [c56] [c55] [c54] [c53] [c52] [c51] [c50] [i8] [i7] [i6] [c49] [c48] [c47] [c46] [c45] [c44] [c43] [i5] [i4] [i3] [c40] [c39] [c38] [c37] [p1] [c36] [c35] [j10] [j9] [c34] [c33] [c32] [c31] [i2] [j8] [c30] [c29] [c28] [c27] [i1] [c25] [c23] [j4] [c21] [c19] [c14] [c12] [j1] [c9] [c8] [c7] [c6] [c2]
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