On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
Realizable and Unrealizable Specifications of Reactive Systems
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Simple Linear-Time Algorithms for Minimal Fixed Points (Extended Abstract)
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Efficient Büchi Automata from LTL Formulae
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Alternating Refinement Relations
CONCUR '98 Proceedings of the 9th International Conference on Concurrency Theory
Automata logics, and infinite games: a guide to current research
Automata logics, and infinite games: a guide to current research
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Efficient on-the-fly algorithms for the analysis of timed games
CONCUR 2005 - Concurrency Theory
Optimizations for LTL Synthesis
FMCAD '06 Proceedings of the Formal Methods in Computer Aided Design
Specify, Compile, Run: Hardware from PSL
Electronic Notes in Theoretical Computer Science (ENTCS)
On the complexity of omega -automata
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
An Antichain Algorithm for LTL Realizability
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Co-ing Büchi Made Tight and Useful
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Compositional Control Synthesis for Partially Observable Systems
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Improved algorithms for the automata-based approach to model-checking
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
Church's problem and a tour through automata theory
Pillars of computer science
Compositional algorithms for LTL synthesis
ATVA'10 Proceedings of the 8th international conference on Automated technology for verification and analysis
Antichains: a new algorithm for checking universality of finite automata
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Safraless compositional synthesis
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Synthesis of reactive(1) designs
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Antichain algorithms for finite automata
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Acacia+, a tool for LTL synthesis
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Synthesis from LTL specifications with mean-payoff objectives
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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In this paper, we present new monolithic and compositional algorithms to solve the LTL realizability problem. Those new algorithms are based on a reduction of the LTL realizability problem to a game whose winning condition is defined by a universal automaton on infinite words with a k-co-Büchi acceptance condition. This acceptance condition asks that runs visit at most k accepting states, so it implicitly defines a safety game. To obtain efficient algorithms from this construction, we need several additional ingredients. First, we study the structure of the underlying automata constructions, and we show that there exists a partial order that structures the state space of the underlying safety game. This partial order can be used to define an efficient antichain algorithm. Second, we show that the algorithm can be implemented in an incremental way by considering increasing values of k in the acceptance condition. Finally, we show that for large LTL formulas that are written as conjunctions of smaller formulas, we can solve the problem compositionally by first computing winning strategies for each conjunct that appears in the large formula. We report on the behavior of those algorithms on several benchmarks. We show that the compositional algorithms are able to handle LTL formulas that are several pages long.