Subrecursive Programming Languages, Part I: efficiency and program structure
Journal of the ACM (JACM)
Reversal-Bounded Multicounter Machines and Their Decision Problems
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
An NP-complete number-theoretic problem
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
The complexity of loop programs
ACM '67 Proceedings of the 1967 22nd national conference
SUPER-EXPONENTIAL COMPLEXITY OF PRESBURGER ARITHMETIC
SUPER-EXPONENTIAL COMPLEXITY OF PRESBURGER ARITHMETIC
WMP '00 Proceedings of the Workshop on Multiset Processing: Multiset Processing, Mathematical, Computer Science, and Molecular Computing Points of View
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It is shown that the class of relations (functions) definable by Presburger formulas is exactly the class of relations (functions) computable by finite-reversal multicounter machines. An upper bound of 2c(N/logN)4 on the deterministic time complexity of the equivalence problem for such machines is established. In fact, it is proved that the inequivalence problem is NP-complete. These results are used to derive some upper bounds on the complexity of the equivalence problem for semilinear sets and simple programs. For example, it is shown that the equivalence problem for semilinear sets (these sets are exactly the Presburger relations) is decidable in deterministic time 22cN2. A class of programs which realize exactly the relations (functions) definable by Presburger formulas is shown to have an NP-complete inequivalence problem. Hence, its equivalence problem is decidable in deterministic time 2p(N). This bound is a four-level exponential improvement over a previously known result.