Abstract
In automated deduction it is sometimes helpful to compute modulo a set E of equations. In this paper we consider the case where E consists of permutation equations only. Here a permutation equation has the form f(x 1,...,x n )=f(x π(1),...,x π( n)) where π is a permutation on {1,...,n}. If E is allowed to be part of the input then even testing E-equality is at least as hard as testing for graph isomorphism. For a fixed set E we present a polynomial time algorithm for testing E-equality. Testing matchability and unifiability is NP-complete. We present relatively efficient algorithms for these problems. These algorithms are based on knowledge from group theory.
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Avenhaus, J. (2004). Efficient Algorithms for Computing Modulo Permutation Theories. In: Basin, D., Rusinowitch, M. (eds) Automated Reasoning. IJCAR 2004. Lecture Notes in Computer Science(), vol 3097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25984-8_31
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DOI: https://doi.org/10.1007/978-3-540-25984-8_31
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