Weighted Pushdown Systems with Indexed Weight Domains

TL;DR

This paper generalizes weighted pushdown systems by introducing indexed semirings and local boundedness, enhancing their applicability in recursive program analysis.

Contribution

It extends weighted pushdown systems with monoid-indexed semirings and relaxes boundedness constraints, broadening their theoretical framework.

Findings

Introduces stack signatures to summarize pushdown computations.

Formulates pushdown systems as automata over monoids.

Generalizes weighted pushdown systems with indexed semirings and local boundedness.

Abstract

The reachability analysis of weighted pushdown systems is a very powerful technique in verification and analysis of recursive programs. Each transition rule of a weighted pushdown system is associated with an element of a bounded semiring representing the weight of the rule. However, we have realized that the restriction of the boundedness is too strict and the formulation of weighted pushdown systems is not general enough for some applications. To generalize weighted pushdown systems, we first introduce the notion of stack signatures that summarize the effect of a computation of a pushdown system and formulate pushdown systems as automata over the monoid of stack signatures. We then generalize weighted pushdown systems by introducing semirings indexed by the monoid and weaken the boundedness to local boundedness.