The concurrency complexity for the Horn fragment of linear logic
The provability problem for the Horn fragment of linear logic is NP-complete [4, 1]. In this work we investigate various definitions of concurrency proposed in  and establish the complexity of the provability problem and the problem of concurrency recognition. The notion of k-maximal concurrency is introduced which guarantees polynomial time provability. Theorems on hierarchy and on complexity of recognition of the property are proved.
Unable to display preview. Download preview PDF.
- 1.Archangelsky D.A., Taitslin M.A., Linear Logic With Fixed Resources. Annals of Pure and Applied Logic, v. 67 (1994),pp. 3–28.Google Scholar
- 2.Archangelsky D.A., Dekhtyar M.I., Kruglov E., Musikaev I.Kh., and Taitslin M.A. Concurrency problem for Horn fragment of Girard's Linear Logic. Logical Foundation of Computer Science, St.Petersburg'94, Lecture Notes in Computer Science, N 813, 1994, pp. 18–22.Google Scholar
- 3.Garey M.R., Johnson D.S. Computers and Intractability. A Guide to the Theory of NP-Completeness. W.H.Freeman and Company, San Francisco, 1979.Google Scholar
- 4.Kanovich M.I. Horn Programming in Linear Logic is NP-complete. Proc.7-th Annual IEEE Symposium on Logic in Computer Science, 1992, pp. 200–210.Google Scholar
- 5.Lincoln P., Mitchell J., Scerdov A., and Shankar N. Decision Problems for Propositional Linear Logic. Proc.31-th IEEE Symposium on Foundation of Computer Science, 1990, pp. 662–671.Google Scholar
- 6.Meyer A.R., Stockmeyer L. J. The equivalence problem for regular expressions with squaring requires exponential time. Proc.13th Ann. Symp. on Switching and Automata Theory, 1972, pp. 125–129.Google Scholar