DeepAI
Log In Sign Up

Model Checking for Fragments of Halpern and Shoham's Interval Temporal Logic Based on Track Representatives

09/06/2017
by   Alberto Molinari, et al.
0

Model checking allows one to automatically verify a specification of the expected properties of a system against a formal model of its behaviour (generally, a Kripke structure). Point-based temporal logics, such as LTL, CTL, and CTL*, that describe how the system evolves state-by-state, are commonly used as specification languages. They proved themselves quite successful in a variety of application domains. However, properties constraining the temporal ordering of temporally extended events as well as properties involving temporal aggregations, which are inherently interval-based, can not be properly dealt with by them. Interval temporal logics (ITLs), that take intervals as their primitive temporal entities, turn out to be well-suited for the specification and verification of interval properties of computations (we interpret all the tracks of a Kripke structure as computation intervals). We study the model checking problem for some fragments of Halpern and Shoham's modal logic of time intervals (HS). HS features one modality for each possible ordering relation between pairs of intervals (the so-called Allen's relations). First, we describe an EXPSPACE model checking algorithm for the HS fragment of Allen's relations meets, met-by, starts, started-by, and finishes, which exploits the possibility of finding, for each track (of unbounded length), an equivalent bounded-length track representative. While checking a property, it only needs to consider tracks whose length does not exceed the given bound. We prove the model checking problem for such a fragment to be PSPACE-hard. Finally, we identify other well-behaved HS fragments which are expressive enough to capture meaningful interval properties of systems, such as mutual exclusion, state reachability, and non-starvation, and whose complexity is less than or equal to that of LTL.

READ FULL TEXT

page 1

page 2

page 3

page 4

01/12/2019

Model checking: the interval way

[...] The most famous MC techniques were developed from the late 80s, be...
06/08/2020

Satisfiability and Model Checking for the Logic of Sub-Intervals under the Homogeneity Assumption

The expressive power of interval temporal logics (ITLs) makes them reall...
11/22/2017

Interval vs. Point Temporal Logic Model Checking: an Expressiveness Comparison

In the last years, model checking with interval temporal logics is emerg...
12/21/2020

Bounded Model Checking of Software Using Interval Methods via Contractors

Bounded model checking (BMC) is a vital technique to find property viola...
02/12/2021

Responsibility and verification: Importance value in temporal logics

We aim at measuring the influence of the nondeterministic choices of a p...
07/17/2013

Model checking coalitional games in shortage resource scenarios

Verification of multi-agents systems (MAS) has been recently studied tak...
06/30/2011

Learning to Order BDD Variables in Verification

The size and complexity of software and hardware systems have significan...