Least and greatest solutions of equations over N

Authors:
Helmut Seidl
Affiliations:
FB IV - Informatik, Universität Trier, D-54286 Trier, Germany
Venue:
Nordic Journal of Computing
Year:
1996

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Abstract

We consider the problem of computing least and greatest solutions of a system of equations xi = fi, i = 1,..., n, over N, i.e., the naturals (extended by ∞), where the right hand sides fi are expressions built up from constants and variables by various sets of operations.We present efficient algorithms in case where the following operations occur: (1) minimum and maximum; (2) maximum, addition and multiplication; (3) minimum, addition and multiplication; (4) minimum, maximum, addition and multiplication. We extend the methods to the cases where (one-sided) conditionals are allowed as well.