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## On the application of substitution algebra to program unification.

#### Abstract

Many problems in software engineering such as program refactoring, deobfuscation, vulnerability detection, require an efficient toolset for detecting pieces of code that have similar behavior. Current state of art in software clone detection makes it possible to find out only those pieces of code which have the same syntactic structure since. A more profound analysis of functional properties of programs encounters with undecidability of equivalence checking problem for Turing-complete models of computation. To overcome this principal deficiency of modern clone detection techniques we suggest to use equivalence relations on programs that are more strong than functional equivalence. One of such equivalences is a so called logic&term program equivalence introduced by V.E. Itkin in 1972 г. In this paper we build a new algorithm for checking logic&term equivalence of programs. This algorithm is based on the operations for computing the least upper bound and the greatest upper bound in the lattice of finite substitutions. Using this algorithm we also develop a procedure for solving the unification problem for sequential programs, i.e. the problem of computing the most general common instance (specialization) of a given pair of programs (pieces of code).

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#### Edition

Proceedings of the Institute for System Programming, vol. 21, 2011, pp. 141-166.

ISSN 2220-6426 (Online), ISSN 2079-8156 (Print).