On Probabilistic Term Rewriting

TL;DR

This paper investigates the termination problem in probabilistic term rewrite systems, introducing novel interpretation methods and analyzing their effectiveness in capturing probabilistic computation and termination properties.

Contribution

It proves the soundness and completeness of the interpretation method for probabilistic termination and analyzes polynomial and matrix interpretations for automated reasoning.

Findings

Interpretation method is sound and complete for probabilistic termination.

Polynomial and matrix interpretations effectively analyze probabilistic rewrite systems.

Probabilistic computation is captured via multidistribution reduction sequences.

Abstract

We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite systems are considered. Two instances of the interpretation method - polynomial and matrix interpretations - are analyzed and shown to capture interesting and nontrivial examples when automated. We capture probabilistic computation in a novel way by way of multidistribution reduction sequences, this way accounting for both the nondeterminism in the choice of the redex and the probabilism intrinsic in firing each rule.