Pure future local temporal logics are expressively complete for Mazurkiewicz traces

Volker Diekert, Paul Gastin
2006 Information and Computation  
The paper settles a long standing problem for Mazurkiewicz traces: the pure future local temporal logic defined with the basic modalities exists-next and until is expressively complete. This means every first-order definable language of Mazurkiewicz traces can be defined in a pure future local temporal logic. The analogous result with a global interpretation has been known, but the treatment of a local interpretation turned out to be much more involved. Local logics are interesting because both
more » ... the satisfiability problem and the model checking problem are solvable in Pspace for these logics whereas they are non-elementary for global logics. Both, the (previously known) global and the (new) local results generalize Kamp's Theorem for words, because for sequences local and global viewpoints coincide.
doi:10.1016/j.ic.2006.07.002 fatcat:lebsg4ijfjcudg2gw2i5mlbqfa