Decidability of Reachability for Polymorphic Systems with Arrays: A Complete Classification

  • Authors:
  • Ranko Lazić

  • Affiliations:
  • Department of Computer Science, University of Warwick, UK

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2005

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Abstract

Many interesting systems can be seen as having two kinds of state variables: array variables, which are mappings from one data type into another; and basic variables, which are used to control the system, to perform basic computations, and for operations involving arrays. We investigate such systems where:*the type of each basic variable is built from type variables using product and sum constructs; *the type of each array variable is B-B^', where B and B^' are types as for basic variables; *on any type variable, either no operations are available, or only the equality predicate, or only a linear-order predicate; *type variables denote arbitrary non-empty finite sets. We present a complete classification of reachability decision problems for these systems into decid- able or undecidable.