The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
Advances in Petri nets 1986, part II on Petri nets: applications and relationships to other models of concurrency
Factorization forests of finite height
Theoretical Computer Science - Special issue on theoretical computer science, algebra and combinatorics
Handbook of theoretical computer science (vol. B)
Theoretical Computer Science
Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
Temporal logic (vol. 1): mathematical foundations and computational aspects
Temporal logic (vol. 1): mathematical foundations and computational aspects
Logical definability on infinite traces
ICALP Selected papers of the twentieth international colloquium on Automata, languages and programming
Languages, automata, and logic
Handbook of formal languages, vol. 3
Parallel Program Schemata and Maximal Parallelism I. Fundamental Results
Journal of the ACM (JACM)
Automata, Languages, and Machines
Automata, Languages, and Machines
The Book of Traces
LTL is expressively complete for Mazurkiewicz traces
Journal of Computer and System Sciences
First-order logic with two variables and unary temporal logic
Information and Computation - Special issue: LICS'97
An Exprssively Complete Linear Time Temporal Logic for Mazurkiewicz Traces.
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
On factorization forests of finite height
Theoretical Computer Science
Pure future local temporal logics are expressively complete for Mazurkiewicz traces
Information and Computation
On First-Order Fragments for Mazurkiewicz Traces
Fundamenta Informaticae - Half a Century of Inspirational Research: Honoring the Scientific Influence of Antoni Mazurkiewicz
Polynomials, fragments of temporal logic and the variety DA over traces
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
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We summarize several characterizations, inclusions, and separations on fragments of first-order logic over words and Mazurkiewicz traces. The results concerning Mazurkiewicz traces can be seen as generalizations of those for words. It turns out that over traces it is crucial, how easy concurrency can be expressed. Since there is no concurrency in words, this distinction does not occur there. In general, the possibility of expressing concurrency also increases the complexity of the satisfiability problem. In the last section we prove an algebraic and a language theoretic characterization of the fragment Σ2[E] over traces. Over words the relation E is simply the order of the positions. The algebraic characterization yields decidability of the membership problem for this fragment. For words this result is well-known, but although our proof works in a more general setting it is quite simple and direct. An essential step in the proof consists of showing that every homomorphism from a free monoid to a finite aperiodic monoid M admits a factorization forest of finite height. We include a simple proof that the height is bounded by 3 |M|.