Temporal logic (vol. 1): mathematical foundations and computational aspects
Temporal logic (vol. 1): mathematical foundations and computational aspects
The Monadic Quantifier Alternation Hierarchy over Graphs is Infinite
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
The complexity of translating logic to finite automata
Automata logics, and infinite games
A Robust Class of Context-Sensitive Languages
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
An Infinite Automaton Characterization of Double Exponential Time
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Emptiness of Multi-pushdown Automata Is 2ETIME-Complete
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Adding nesting structure to words
Journal of the ACM (JACM)
Context-bounded analysis of concurrent queue systems
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Uniform satisfiability problem for local temporal logics over Mazurkiewicz traces
Information and Computation
The tree width of auxiliary storage
Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Temporal logics for concurrent recursive programs: satisfiability and model checking
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Reachability of multistack pushdown systems with scope-bounded matching relations
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
Context-Bounded model checking of concurrent software
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
MSO decidability of multi-pushdown systems via split-width
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
Linear-Time model-checking for multithreaded programs under scope-bounding
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
A temporal logic for multi-threaded programs
TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
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We consider the linear-time model checking problem for boolean concurrent programs with recursive procedure calls. While sequential recursive programs are usually modeled as pushdown automata, concurrent recursive programs involve several processes and can be naturally abstracted as pushdown automata with multiple stacks. Their behavior can be understood as words with multiple nesting relations, each relation connecting a procedure call with its corresponding return. To reason about multiply nested words, we consider the class of all temporal logics as defined in the book by Gabbay, Hodkinson, and Reynolds (1994). The unifying feature of these temporal logics is that their modalities are defined in monadic second-order (MSO) logic. In particular, this captures numerous temporal logics over concurrent and/or recursive programs that have been defined so far. Since the general model checking problem is undecidable, we restrict attention to phase bounded executions as proposed by La Torre, Madhusudan, and Parlato (LICS 2007). While the MSO model checking problem in this case is non-elementary, our main result states that the model checking (and satisfiability) problem for all MSO-definable temporal logics is decidable in elementary time. More precisely, it is solvable in (n+2)-EXPTIME where n is the maximal level of the MSO modalities in the monadic quantifier alternation hierarchy. We complement this result and provide, for each level n, a temporal logic whose model checking problem is n-EXPSPACE-hard.