Elementary Deduction Problem for Locally Stable Theories with Normal Forms

Mauricio Ayala-Rincón
(Universidade de Brasília)
Maribel Fernández
(King's College London)
Daniele Nantes-Sobrinho
(Universidade de Brasília)

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.

In Delia Kesner and Petrucio Viana: Proceedings Seventh Workshop on Logical and Semantic Frameworks, with Applications (LSFA 2012), Rio de Janeiro, Brazil, September 29-30, 2012, Electronic Proceedings in Theoretical Computer Science 113, pp. 45–60.
Published: 28th March 2013.

ArXived at: http://dx.doi.org/10.4204/EPTCS.113.7 bibtex PDF
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