A new algorithm for strategy synthesis in LTL games

  • Authors:

  • Aidan Harding;Mark Ryan;Pierre-Yves Schobbens

  • Affiliations:

  • School of Computer Science, The University of Birmingham, Edgbaston, Birmingham, UK;School of Computer Science, The University of Birmingham, Edgbaston, Birmingham, UK;Institut d'Informatique, Facultés Universitaires de Namur, Namur, Belgium

  • Venue:
  • TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
  • Year:
  • 2005

Quantified Score

Hi-index 0.00

Visualization

Abstract

The automatic synthesis of programs from their specifications has been a dream of many researchers for decades. If we restrict to open finite-state reactive systems, the specification is often presented as an ATL or LTL formula interpreted over a finite-state game. The required program is then a strategy for winning this game. A theoretically optimal solution to this problem was proposed by Pnueli and Rosner, but has never given good results in practice. This is due to the 2EXPTIME-complete complexity of the problem, and the intricate nature of Pnueli and Rosner's solution. A key difficulty in their procedure is the determinisation of Büchi automata. In this paper we look at an alternative approach which avoids determinisation, using instead a procedure that is amenable to symbolic methods. Using an implementation based on the BDD package CuDD, we demonstrate its scalability in a number of examples. Furthermore, we show a class of problems for which our algorithm is singly exponential. Our solution, however, is not complete; we prove a condition which guarantees completeness and argue by empirical evidence that examples for which it is not complete are rare enough to make our solution a useful tool.