Faster and Better Simple Temporal Problems

Abstract

In this paper we give a structural characterization and extend the tractability frontier of the Simple Temporal Problem (STP) by defining the class of the Extended Simple Temporal Problem (ESTP), which augments STP with strict inequalities and monotone Boolean formulae on inequations (i.e., formulae involving the operations of conjunction, disjunction and parenthesization). A polynomial-time algorithm is provided to solve ESTP, faster than previous state-of-the-art algorithms for other extensions of STP that had been considered in the literature, all encompassed by ESTP. We show the practical competitiveness of our approach through a proof-of-concept implementation and an experimental evaluation involving also state-of-the-art SMT solvers.

A Logic of East and West

“…More recently, Ostuni et al (2021) proposed a faster polynomial-time algorithm to solve a finite set of inequalities of the form (x − y) ∼ c, where x, y are real variables, ∼ is ≤ or <, and c is a real number. The time complexity of the algorithm is O(nn ), where n is the number of real variables and n is the number of inequalities in the finite set.…”

“…Consider any L(LEW ) formula in disjunctive normal form φ 1 ∨• • •∨φ m , where m > 0 and every literal is of one of the forms: W (a, b), E(a, b), dW (a, b), dE (a, b) and their negations. Then, by Koubarakis and Skiadopoulos (2000), the satisfiability problem for any disjunct φ i , where 1 ≤ i ≤ m, is decidable in O(n 3 ) time; more precisely, by Ostuni et al (2021), it is in O(nn ), where n is the number of variables, n is the number of inequalities.…”

“…Differing from the work on disjunctive linear relations (Jonsson & Bäckström, 1998), linear constraints (Koubarakis & Skiadopoulos, 2000;Ostuni et al, 2021) and the INDU calculus (Pujari et al, 1999), we take an axiomatisation-based approach and explore the existence of finite sound and complete axiomatisations of LEW , with the aim of developing rule-based reasoners based on a complete set of axioms as was done by Du et al (2015).…”