“Sometimes” and “not never” revisited: on branching versus linear time temporal logic
Journal of the ACM (JACM) - The MIT Press scientific computation series
Automata-Theoretic techniques for modal logics of programs
Journal of Computer and System Sciences
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
Infinitary languages: basic theory and applications to concurrent systems
Current trends in concurrency. Overviews and tutorials
Handbook of theoretical computer science (vol. B)
The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
Information Processing Letters
Reasoning about infinite computations
Information and Computation
Computer-aided verification of coordinating processes: the automata-theoretic approach
Computer-aided verification of coordinating processes: the automata-theoretic approach
Formal verification by symbolic evaluation of partially-ordered trajectories
Formal Methods in System Design - Special issue on symbolic model checking
An automata-theoretic approach to linear temporal logic
Proceedings of the VIII Banff Higher order workshop conference on Logics for concurrency : structure versus automata: structure versus automata
Handbook of formal languages, vol. 3
The modal mu-calculus alternation hierarchy is strict
Theoretical Computer Science
Symbolic model checking using SAT procedures instead of BDDs
Proceedings of the 36th annual ACM/IEEE Design Automation Conference
Model checking
An automata-theoretic approach to branching-time model checking
Journal of the ACM (JACM)
"Sometime" is sometimes "not never": on the temporal logic of programs
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Automata for the Modal mu-Calculus and related Results
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps
FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
Generalized Symbolic Trajectory Evaluation - Abstraction in Action
FMCAD '02 Proceedings of the 4th International Conference on Formal Methods in Computer-Aided Design
Safety for Branching Time Semantics
ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
The anchored version of the temporal framework
Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, School/Workshop
Safety and Liveness in Branching Time
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Finite automata and their decision problems
IBM Journal of Research and Development
Classifying discrete temporal properties
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Eliminating recursion in the µ-calculus
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Model Checking Linear Properties of Prefix-Recognizable Systems
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
An automata-theoretic approach to infinite-state systems
Time for verification
Antichains and compositional algorithms for LTL synthesis
Formal Methods in System Design
On locally checkable properties
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
On the construction of fine automata for safety properties
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
On the succinctness of nondeterminism
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
Logical refinements of Church's problem
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
HVC'12 Proceedings of the 8th international conference on Hardware and Software: verification and testing
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Bounded model checking methodologies check the correctness of a system with respect to a given specification by examining computations of a bounded length. Results from set-theoretic topology imply that sets in Σω that are both open and closed (clopen sets) are precisely bounded sets: membership of a word in a clopen set can be determined by examining a bounded prefix of it. Clopen sets correspond to specifications that are both safety and co-safety. In this paper we study bounded specifications from this perspective. We consider both the linear and the branching frameworks. In the linear framework, we show that when clopen specifications are given by word automata or temporal logic formulas, we can identify a bound and translate the specification to bounded formalisms such as cycle-free automata and bounded LTL. In the branching framework, we show that while clopen sets of trees with infinite branching degrees may not be bounded, we can extend the results from the linear framework to clopen specifications given by tree automata or temporal logic formulas, even for trees with infinite branching degrees. There, we can identify a bound and translate clopen specifications to cycle-free automata and modal logic. Finally, we show how our results imply that the bottom levels of the µ-calculus hierarchy coalesce.