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Nominal Logic: A First Order Theory of Names and Binding
 Information and Computation
, 2001
"... This paper formalises within firstorder logic some common practices in computer science to do with representing and reasoning about syntactical structures involving named bound variables (as opposed to nameless terms, explicit substitutions, or higher order abstract syntax). It introduces Nominal L ..."
Abstract

Cited by 176 (15 self)
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This paper formalises within firstorder logic some common practices in computer science to do with representing and reasoning about syntactical structures involving named bound variables (as opposed to nameless terms, explicit substitutions, or higher order abstract syntax). It introduces Nominal Logic, a version of firstorder manysorted logic with equality containing primitives for renaming via nameswapping and for freshness of names, from which a notion of binding can be derived. Its axioms express...
Computing Conjugacy Classes of Elements in Matrix Groups
"... This article describes a setup that – given a composition tree – provides functionality for calculation in finite matrix groups using the TrivialFitting approach that has been used successfully for permutation groups. It treats the composition tree as a blackbox object. It thus is applicable to ot ..."
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This article describes a setup that – given a composition tree – provides functionality for calculation in finite matrix groups using the TrivialFitting approach that has been used successfully for permutation groups. It treats the composition tree as a blackbox object. It thus is applicable to other classes of groups for which a composition tree can be obtained. As an example, we consider an effective algorithm for determining conjugacy class representatives. Keywords:
Constructive
"... recognition of classical groups in odd characteristic C.R. LeedhamGreen and E.A. O’Brien Let G = 〈X 〉 ≤ GL(d, F) be a classical group in its natural representation defined over a finite field F of odd characteristic. We present Las Vegas algorithms to construct standard generators for G which per ..."
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recognition of classical groups in odd characteristic C.R. LeedhamGreen and E.A. O’Brien Let G = 〈X 〉 ≤ GL(d, F) be a classical group in its natural representation defined over a finite field F of odd characteristic. We present Las Vegas algorithms to construct standard generators for G which permit us to write an element of G as a straightline program in X. The algorithms run in polynomialtime, subject to the existence of a discrete logarithm oracle for F. 1