“Sometimes” and “not never” revisited: on branching versus linear time temporal logic
Journal of the ACM (JACM) - The MIT Press scientific computation series
Automatic verification of finite-state concurrent systems using temporal logic specifications
ACM Transactions on Programming Languages and Systems (TOPLAS)
Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Computation tree logic CTL* and path quantifiers in the monadic theory of the binary tree
14th International Colloquium on Automata, languages and programming
Complementing deterministic Bu¨chi automata in polynomial time
Journal of Computer and System Sciences
Alternating automata on infinite trees
Theoretical Computer Science
Handbook of theoretical computer science (vol. B)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Symbolic model checking: 1020 states and beyond
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
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
IEEE Transactions on Software Engineering - Special issue on formal methods in software practice
CTL and equivalent sublanguages of CTL
CHDL'97 Proceedings of the IFIP TC10 WG10.5 international conference on Hardware description languages and their applications : specification, modelling, verification and synthesis of microelectronic systems: specification, modelling, verification and synthesis of microelectronic systems
Checking that finite state concurrent programs satisfy their linear specification
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Journal of the ACM (JACM)
Model checking
An automata-theoretic approach to branching-time model checking
Journal of the ACM (JACM)
A New Heuristic for Bad Cycle Detection Using BDDs
Formal Methods in System Design - Special issue on CAV '97
Weak alternating automata are not that weak
ACM Transactions on Computational Logic (TOCL)
Symbolic Model Checking
Automata for the Modal mu-Calculus and related Results
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
Alternating Automata. The Weak Monadic Theory of the Tree, and its Complexity
ICALP '86 Proceedings of the 13th International Colloquium on Automata, Languages and Programming
Deterministic w Automata vis-a-vis Deterministic Buchi Automata
ISAAC '94 Proceedings of the 5th International Symposium on Algorithms and Computation
Relating linear and branching model checking
PROCOMET '98 Proceedings of the IFIP TC2/WG2.2,2.3 International Conference on Programming Concepts and Methods
A Linear-Time Model-Checking Algorithm for the Alternation-Free Modal Mu-Calculus
CAV '91 Proceedings of the 3rd International Workshop on Computer Aided Verification
The Rabin Index and Chain Automata, with Applications to Automatas and Games
Proceedings of the 7th International Conference on Computer Aided Verification
VIS: A System for Verification and Synthesis
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Expressibility results for linear-time and branching-time logics
Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, School/Workshop
Efficient model checking via the equational /spl mu/-calculus
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Relating word and tree automata
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
The common fragment of CTL and LTL
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Synthesis of communicating processes from temporal logic specifications
Synthesis of communicating processes from temporal logic specifications
On the Relative Succinctness of Nondeterministic Büchi and co-Büchi Word Automata
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Computable CTL* for Discrete-Time and Continuous-Space Dynamic Systems
RP '09 Proceedings of the 3rd International Workshop on Reachability Problems
Automata-theoretic model checking revisited
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Synthesis of trigger properties
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
The quest for a tight translation of büchi to co-büchi automata
Fields of logic and computation
The blow-up in translating LTL to deterministic automata
MoChArt'10 Proceedings of the 6th international conference on Model checking and artificial intelligence
An O(n2) time algorithm for alternating Büchi games
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Translating to Co-Büchi Made Tight, Unified, and Useful
ACM Transactions on Computational Logic (TOCL)
Tightening the exchange rates between automata
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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Model checking is a method for the verification of systems with respect to their specifications. Symbolic model-checking, which enables the verification of large systems, proceeds by calculating fixed-point expressions over the system's set of states. The μ-calculus is a branching-time temporal logic with fixed-point operators. As such, it is a convenient logic for symbolic model-checking tools. In particular, the alternation-free fragment of μ-calculus has a restricted syntax, making the symbolic evaluation of its formulas computationally easy. Formally, it takes time that is linear in the size of the system. On the other hand, specifiers find the μ-calculus inconvenient. In addition, specifiers often prefer to use linear-time formalisms. Such formalisms, however, cannot in general be translated to the alternation-free μ-calculus, and their symbolic evaluation involves nesting of fixed-points, resulting in time complexity that is quadratic in the size of the system. In this article, we characterize linear-time properties that can be specified in the alternation-free μ-calculus. We show that a linear-time property can be specified in the alternation-free μ-calculus iff it can be recognized by a deterministic Büchi automaton. We study the problem of deciding whether a linear-time property, specified by either an automaton or an LTL formula, can be translated to an alternation-free μ-calculus formula, and describe the translation, when possible.