Elementary Deduction Problem for Locally Stable Theories with Normal Forms
This work addresses a specific problem in automated deduction and cryptographic protocol analysis, representing an incremental extension of existing results.
The authors tackled the intruder deduction problem for locally stable theories with normal forms by developing an algorithm that combines AC-matching and linear Diophantine equations, and applied it to blind signatures to extend previous decidability results.
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.