The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
Automata-Theoretic techniques for modal logics of programs
Journal of Computer and System Sciences
The complementation problem for Bu¨chi automata with applications to temporal logic
Theoretical Computer Science
On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
On the development of reactive systems
Logics and models of concurrent systems
Reasoning about infinite computations
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Automata on Infinite Objects and Church's Problem
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FoSSaCS '01 Proceedings of the 4th International Conference on Foundations of Software Science and Computation Structures
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PROCOMET '98 Proceedings of the IFIP TC2/WG2.2,2.3 International Conference on Programming Concepts and Methods
Efficient Decision Procedures for Model Checking of Linear Time Logic Properties
CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
Finding the Causes of Unrealizability of Reactive System Formal Specifications
SEFM '04 Proceedings of the Software Engineering and Formal Methods, Second International Conference
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps
Formal Methods in System Design
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LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Optimizations for LTL Synthesis
FMCAD '06 Proceedings of the Formal Methods in Computer Aided Design
A Practical Introduction to PSL (Series on Integrated Circuits and Systems)
A Practical Introduction to PSL (Series on Integrated Circuits and Systems)
Interactive presentation: Automatic hardware synthesis from specifications: a case study
Proceedings of the conference on Design, automation and test in Europe
Specify, Compile, Run: Hardware from PSL
Electronic Notes in Theoretical Computer Science (ENTCS)
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
The complexity of tree automata and logics of programs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
Anzu: a tool for property synthesis
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Safraless compositional synthesis
CAV'06 Proceedings of the 18th 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
A Framework for Inherent Vacuity
HVC '08 Proceedings of the 4th International Haifa Verification Conference on Hardware and Software: Verification and Testing
Compositional algorithms for LTL synthesis
ATVA'10 Proceedings of the 8th international conference on Automated technology for verification and analysis
Antichains and compositional algorithms for LTL synthesis
Formal Methods in System Design
Robustness in the presence of liveness
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Towards a notion of unsatisfiable and unrealizable cores for LTL
Science of Computer Programming
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
HVC'12 Proceedings of the 8th international conference on Hardware and Software: verification and testing
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We argue that the usual trace-based notions of implication and equivalence for linear temporal logics are too strong and should be complemented by the weaker notions of open implication and open equivalence. Although open implication is harder to compute, it can be used to advantage both in model checking and in synthesis. We study the difference between trace-based equivalence and open equivalence and describe an algorithm to compute open implication of Linear Temporal Logic formulas with an asymptotically optimal complexity. We also show how to compute open implication while avoiding Safra's construction. We have implemented an open-implication solver for Generalized Reactivity(1) specifications. In a case study, we show that open equivalence can be used to justify the use of an alternative specification that allows us to synthesize much smaller systems in far less time.