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
Reasoning about networks with many identical finite-state processes
PODC '86 Proceedings of the fifth annual ACM symposium on Principles of distributed computing
The complementation problem for Bu¨chi automata with applications to temporal logic
Theoretical Computer Science
The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
Reasoning about systems with many processes
Journal of the ACM (JACM)
Model checking and abstraction
ACM Transactions on Programming Languages and Systems (TOPLAS)
Temporal logic in information systems
Logics for databases and information 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
Model checking
Towards Regular Languages over Infinite Alphabets
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Hybrid Automata with Finite Bisimulatioins
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
An Automata-Theoretic Approach to Constraint LTL
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Efficient Algorithms for Model Checking Pushdown Systems
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Proceedings of the 7th International Conference on Computer Aided Verification
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Variable automata over infinite alphabets
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
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In classical LTL model checking, both the system and the specification are over a finite set of atomic propositions. We present a natural extension of this model, in which the atomic propositions are parameterized by variables ranging over some (possibly infinite) domain. For example, by parameterizing the atomic propositions send and receive by a variable x ranging over possible messages, the specification ${\textsf{G} } ({\it send}.x \rightarrow{\textsf{F} }{\it receive}.x)$ specifies that not only each send signal is followed by a receive signal, but also that the content of the received message agrees with the content of the one sent. Our extended setting consists of Variable LTL (VLTL) --- a specification formalism that extends LTL with atomic propositions parameterized by variables, and abstract systems --- systems in which atomic propositions may be parameterized by variables. We study the model-checking problem in this setting. We show that while the general setting is undecidable, some useful special cases are decidable. In particular, for fragments of VLTL that restrict the quantification over the variables, the model checking is PSPACE-complete, and thus is not harder than the LTL model checking problem. The latter result conveys the strength and advantage of our setting.