Decision Procedures for Queues with Integer Constraints

  • Ting Zhang
  • Henny B. Sipma
  • Zohar Manna
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3821)


Queues are a widely used data structure in programming languages. They also provide an important synchronization mechanism in modeling distributed protocols. In this paper we extend the theory of queues with a length function that maps a queue to its size, resulting in a combined theory of queues and Presburger arithmetic. This extension provides a natural but tight coupling between the two theories, and hence the general Nelson-Oppen combination method for decision procedures is not applicable. We present a decision procedure for the quantifier-free theory and a quantifier elimination procedure for the first-order theory that can remove a block of existential quantifiers in one step.


Decision Procedure Integer Variable Length Function Elimination Procedure Satisfying Assignment 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ting Zhang
    • 1
  • Henny B. Sipma
    • 1
  • Zohar Manna
    • 1
  1. 1.Computer Science DepartmentStanford University 

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