Elementary Deduction Problem for Locally Stable Theories with Normal Forms

TL;DR

This paper introduces an efficient algorithm for the intruder deduction problem in locally stable theories with normal forms, extending decidability results to theories like blind signatures.

Contribution

It presents a novel algorithm combining AC-matching and linear Diophantine solving to decide IDP for a broad class of theories, including blind signatures.

Findings

Decidable intruder deduction problem for locally stable theories.

Algorithm effectively handles theories with normal forms.

Extended decidability to blind signature theories.

Abstract

We present an algorithm to decide the intruder deduction problem (IDP) for a class of locally stable theories enriched with normal forms. Our result relies on a new and efficient algorithm to solve a restricted case of higher-order associative-commutative matching, obtained by combining the Distinct Occurrences of AC- matching algorithm and a standard algorithm to solve systems of linear Diophantine equations. A translation between natural deduction and sequent calculus allows us to use the same approach to decide the \emphelementary deduction problem for locally stable theories. As an application, we model the theory of blind signatures and derive an algorithm to decide IDP in this context, extending previous decidability results.