Pure future local temporal logics are

Abstract not found

Mazurkiewicz traces ⋆

Abstract. To obtain an expressively complete linear-time temporal logic (LTL) over Mazurkiewicz traces that is computationally tractable, we need to intepret formulas locally, at individual events in a trace, rather than globally, at configurations. Such local logics necessarily require past modalities, in contrast to the classical setting of LTL over sequences. Earlier attempts at defining expressively complete local logics have used very general past modalities as well as filters (side-conditions) that “look sideways ” and talk of concurrent events. In this paper, we show that it is possible to use unfiltered future modalities in conjunction with past constants and still obtain a logic that is expressively complete over traces.

We prove that every rational language of words indexed by linear orderings is definable in monadic second-order logic. We also show that the converse is true for the class of languages indexed by countable scattered linear orderings, but false in the general case. As a corollary we prove that the inclusion problem for rational languages of words indexed by countable linear orderings is decidable.

is permitted for educational or research use on condition that this copyright notice is included in any copy. Publications in the FI MU Report Series are in general accessible via WWW: