Optimal paths in weighted timed automata

  • Authors:

  • Rajeev Alur;Salvatore La Torre;George J. Pappas

  • Affiliations:

  • Department of Computer and Information Science, University of Pennsylvania, 200 South 33rd Street, Philadelphia, PA;Departimento di Informatica ed Applicazioni, Università degli Studi di Salerno, Via Urbano II, Baronissi 84081 (SA), Italy;Department of Electrical and System Engineering, University of Pennsylvania, 200 South 33rd Street, Philadelphia, PA

  • Venue:
  • Theoretical Computer Science - Logic, semantics and theory of programming
  • Year:
  • 2004

Quantified Score

Hi-index 0.00

Visualization

Abstract

We consider the optimal-reachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to computing (parametric) shortest paths in a finite weighted directed graph. We call this graph a parametric sub-region graph. It refines the region graph, a standard tool for the analysis of timed automata, by adding the information which is relevant to solving the optimal-teachability problem. We present an algorithm to solve the optimal-reachability problem for weighted timed automata that takes time exponential in O(n(|δ(A)| + |Wmax|)), where n is the number of clocks, |δ(A)| is the size of the clock constraints and |Wmax| is the size of the largest weight. We show that this algorithm can be improved, if we restrict to weighted timed automata with a single clock. In case we consider a single starting state for the optimal-reachability problem, our approach yields an algorithm that takes exponential time only in the length of clock constraints.