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Exact computation sequences

  • Alex Pelin
  • Jean H. Gallier
Algebraic Theory Of Semantics
Part of the Lecture Notes in Computer Science book series (LNCS, volume 214)

Abstract

Exact computation sequences are sequences of the form
$$< L_0 ,A_0 > \mathop - \limits^{S_1 } > < L_1 ,A_1 > \mathop - \limits^{S_2 } > ...\mathop - \limits^{S_n } > < L_n ,\emptyset > ,$$
, where L0 is a free algebra, A0 is a set of conditional equations over L0, Si is a "step function", L i =S i (L i −1), and A i =S i (A i −1). Each step function is the top-down reduction extension of a set of confluent and noetherian rewrite rules. These sequences are used in solving the word problem for free algebras, since for any pair of terms t1,t2 in L,
$$t_1 = _{A_0 } t_2 iff S_n o...oS_1 \left( {t_1 } \right) = S_n o...oS_1 \left( {t_2 } \right).$$

We analyze properties of exact computation sequences such as: determining the relation between the sets <L i−1 ,A i−1 > and S i , and the output pair <L i ,A i >, and we present criteria for choosing the equations E i in <L i −1,A i −1> which are used to generate the reductions S i . We also give examples showing how to construct exact computation sequences for several axiom systems by applying the properties and the criteria presented in the article.

Keywords

Word Problem Free Algebra Standard Language Automate Deduction Abstract Data Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Alex Pelin
    • 1
  • Jean H. Gallier
    • 2
  1. 1.Department of Mathematical Sciences Tamiami CampusFlorida International UniversityMiami
  2. 2.Department of Computer and Information ScienceUniversity of PennsylvaniaPhiladelphia

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