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A normal form for restricted exponential functions. (English) Zbl 0665.03018
A first order theory G is defined, the terms of which, roughly speaking, can be built as linear combination of “towers of simple exponentiations” with polynomial coefficients. A term rewriting system \({\mathfrak R}\) is introduced, which converts every term of G to its normal form. \({\mathfrak R}\) can be run as it is on a computer in order to solve the identity problem for a subsystem of \(E=<N_+,+,\times,\exp,1>.\) This is done by showing that two terms in G are identical if and only if they have the same normal form with respect to \({\mathfrak R}\).
MSC:
03C05 Equational classes, universal algebra in model theory
68Q65 Abstract data types; algebraic specification
08B05 Equational logic, Mal’tsev conditions
03C07 Basic properties of first-order languages and structures
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References:
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