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We study equations of the form (α=x) which are single axioms for group theory. Earlier examples of such were found by Neumann and McCune. We prove some lower bounds on the complexity of these α, showing that McCune's examples are the shortest possible. We also show that no such α can have only...
Much research has been devoted in building computer systems for checking proofs or for developing interactively correct proofs in specific logical systems. However, implementing a proof environment for a specific logical system is both complex and time-consuming, this-together with the...
We describe an implementation of an extension to the Boyer-Moore Theorem Prover and logic that allows first-order quantification. The extension retains the capabilities of the Boyer-Moore system while allowing the increased flexibility in specification and proof that is provided by quantifiers....
In the 1820s Fourier provided the first algorithm for solving linear arithmetic constraints. In other words, this algorithm determines whether or not the polyhedral set associated with the constraints is empty. We show here that Fourier's algorithm has an important hidden property: in effect it...
The anti-unifier is the dual notion to the unifier, i.e., it is the most specific term that has the input terms as instances. We show that the problem of anti-unification is in NC, in contrast to unification that is known to be P-complete.
In this paper we present optimal processor x time parallel algorithms for term matching and anti-unification of terms represented as trees. Term matching is the special case of unification in which one of the terms is restricted to contain no variables. It has wide applicability to logic...
This article is the twenty-fourth of a series of articles discussing various open research problems in automated reasoning. The problem proposed for research asks one to find an appropriate theory for modulating across argument and across literal boundaries. Because demodulation has proved so...
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