PVM: Parallel virtual machine: a users' guide and tutorial for networked parallel computing
PVM: Parallel virtual machine: a users' guide and tutorial for networked parallel computing
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Symbolic model checking using SAT procedures instead of BDDs
Proceedings of the 36th annual ACM/IEEE Design Automation Conference
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Cryptography: Theory and Practice
Cryptography: Theory and Practice
Representing Arithmetic Constraints with Finite Automata: An Overview
ICLP '02 Proceedings of the 18th International Conference on Logic Programming
Construction of Abstract State Graphs with PVS
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Elementary bounds for presburger arithmetic
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Presburger arithmetic with bounded quantifier alternation
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Predicate Abstraction of ANSI-C Programs Using SAT
Formal Methods in System Design
Deciding Quantifier-Free Presburger Formulas Using Parameterized Solution Bounds
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Termination analysis of imperative programs using bitvector arithmetic
VSTTE'12 Proceedings of the 4th international conference on Verified Software: theories, tools, experiments
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Modular arithmetic is the underlying integral computation model in conventional programming languages. In this paper, we discuss the satisfiability problem of propositional formulae in modular arithmetic over the finite ring $\textbf{Z}_{2^\omega}$. Although an upper bound of $2^{2^{O (n^4)}}$ can be obtained by solving alternation-free Presburger arithmetic, it is easy to see that the problem is in fact NP-complete. Further, we give an efficient reduction to integer programming with the number of constraints and variables linear in the length of the given linear modular arithmetic formula. For non-linear modular arithmetic formulae, an additional factor of ω is needed. With the advent of efficient integer programming packages, our algorithm could be useful to software verification in practice.