Temporal logic of programs
Handbook of theoretical computer science (vol. B)
Reasoning in a restricted temporal logic
Information and Computation
Over words, two variables are as powerful as one quantifier alternation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Specifying Concurrent Program Modules
ACM Transactions on Programming Languages and Systems (TOPLAS)
Automata, Languages, and Machines
Automata, Languages, and Machines
An Until Hierarchy for Temporal Logic
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
First-Order Logic with Two Variables and Unary Temporal
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Temporal logic and semidirect products: an effective characterization of the until hierarchy
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
STeP: The Stanford Temporal Prover
STeP: The Stanford Temporal Prover
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
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We provide an effective characterization of the "until-since hierarchy" of linear temporal logic, that is, we show how to compute for a given temporal property the minimal nesting depth in "until" and "since" required to express it. This settles the most prominent classification problem for linear temporal logic. Our characterization of the individual levels of the "until-since hierarchy" is algebraic: for each n, we present a decidable class of finite semigroups and show that a temporal property is expressible with nesting depth at most n if and only if the syntactic semigroup of the formal language associated with the property belongs to the class provided. The core of our algebraic characterization is a new description of substitution in linear temporal logic in terms of block products of finite semigroups.