On the non-termination of MDG-based abstract state enumeration

  • Authors:
  • Otmane Aït Mohamed;Xiaoyu Song;Eduard Cerny

  • Affiliations:
  • Concordia University, ECE Department, 1455 de Maisonneuve Blvd. W., Montreal, Canada H3G 1M8;Portland State University, P.O. Box 751, Portland, OR;Université of Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, Canada H3C 3J7

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2003

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Abstract

Multiway decision graphs are a new class of decision graphs for representing abstract states machines. This yields a new verification technique that can deal with the data-width problem by using abstract sorts and uninterpreted functions to represent data value and data operations, respectively. However, in many cases, it may suffer from the non-termination of the state enumeration procedure. This paper presents a novel approach to solving the non-termination problem when the generated set of states, even infinite, represents a structured domain where terms (states) share certain repetitive patterns. The approach is based on the schematization method developed by Chen and Hsiang, namely ρ-terms. Schematization provides a suitable formalism for finitely manipulating infinite sets of terms. We illustrate the effectiveness of our method by several examples.