The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
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Temporal logic (vol. 1): mathematical foundations and computational aspects
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Over words, two variables are as powerful as one quantifier alternation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Automata, Languages, and Machines
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LTL is expressively complete for Mazurkiewicz traces
Journal of Computer and System Sciences
An Elementary Expressively Complete Temporal Logic for Mazurkiewicz Traces
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
First-order logic with two variables and unary temporal logic
Information and Computation - Special issue: LICS'97
An Until Hierarchy for Temporal Logic
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
An Exprssively Complete Linear Time Temporal Logic for Mazurkiewicz Traces.
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Pure future local temporal logics are expressively complete for Mazurkiewicz traces
Information and Computation
Polynomials, fragments of temporal logic and the variety DA over traces
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Uniform Satisfiability in PSPACE for Local Temporal Logics Over Mazurkiewicz Traces
Fundamenta Informaticae - Half a Century of Inspirational Research: Honoring the Scientific Influence of Antoni Mazurkiewicz
Structure theorem and strict alternation hierarchy for FO2 on words
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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Mazurkiewicz traces form a model for concurrency. Temporal logic and first-order logic are important tools in order to deal with the abstract behavior of such systems. Since typical properties can be described by rather simple logical formulas one is interested in logical fragments. One focus of this paper is unary temporal logic and first-order logic in two variables. Over words, this corresponds to the variety of finite monoids calledDA. However, overMazurkiewicz traces it is crucial whether traces are given as dependence graphs or as partial orders (over words these notions coincide). The main technical contribution is a generalization of important characterizations of DA from words to dependence graphs, whereas the use of partial orders leads to strictly larger classes. As a consequence we can decide whether a first-order formula over dependence graphs is equivalent to a first-order formula in two variables. The corresponding result for partial orders is not known. This difference between dependence graphs and partial orders also affects the complexity of the satisfiability problems for the fragments under consideration: for first-order formulas in two variables we prove an NEXPTIME upper bound, whereas the corresponding problem for partial orders leads to EXPSPACE. Furthermore, we give several separation results for the alternation hierarchy for first-order logic. It turns out that even for those levels at which one can express the partial order relation in terms of dependence graphs, the fragments over partial orders have more expressive power.