We study translations from Metric Temporal Logic (MTL) over the natural numbers to Linear Temporal Logic (LTL). In particular, we present two approaches for translating from MTL to LTL which preserve the ExpSpace complexity of the satisfiability problem for MTL. In each of these approaches we consider the case where the mapping between states and time points is given by (1) a strict monotonic f...

Linear logic, introduced by Girard in 1987, has been called a resource conscious logic. In order to express a dynamic change in process environment, it is useful to consider a concept of resource such as data consumption. The expressive power of linear logic is evidenced by some very natural encodings of computational models such as Petri nets, counter machines, Turing machines, and others. For...

In this paper we look into the assumption of interpreting LTL over finite traces. In particular we show that LTLf , i.e., LTL under this assumption, is less expressive than what might appear at first sight, and that at essentially no computational cost one can make a significant increase in expressiveness while maintaining the same intuitiveness of LTLf interpreted over finite traces. Indeed, w...

This paper presents a complete axiomatization of fully decid-able propositional real-time linear temporal logics with past: the Event Clock Logic (ECL) and the Metric Interval Temporal Logic with past (MITL). The completeness proof consists of an eeective proof building procedure for ECL. From this result we obtain a complete axiomatization of MITL by providing axioms translating MITL formulae ...

A simple extension of the propositional temporal logic of linear time is proposed. The extension consists of strengthening the until operator by indexing it with the regular programs of propositional dynamic logic (PDL). It is shown that DLTL, the resulting logic, is expressively equivalent to S1S, the monadic second-order theory of ω-sequences. In fact a sublogic of DLTL which corresponds to p...

We present a collection of command-line tools designed to generate, filter, convert, simplify, lists of Linear-time Temporal Logic formulas. These tools were introduced in the release 1.0 of Spot, and we believe they should be of interest to anybody who has to manipulate LTL formulas. We focus on two tools in particular: ltlfilt, to filter and transform formulas, and ltlcross to cross-check LTL...

In the present paper, we introduce the backdoor set approach into the field of temporal logic for the global fragment of linear temporal logic. We study the parameterized complexity of the satisfiability problem parameterized by the size of the backdoor. We distinguish between backdoor detection and evaluation of backdoors into the fragments of Horn and Krom formulas. Here we classify the opera...

We study linear time temporal logics of multiple agents, where the temporal modalities are local. These modalities not only refer to local next-instants and local eventuality, but also global views of agents at any local instant, which are updated due to communication from other agents. Thus agentsalso reason about the future, present and past of other agents in the system. The models for these...