Abstract
The nondeterministic lower space bound \(\sqrt n\) of Hunt, for the problem if a regular expression with intersection describes a non-empty language, is improved to the upper bound n. For the general inequivalence problem for regular expressions with intersection the lower bound cn matches the upper bound except for the constant c. And the proof for this tight lower bound is simpler than the proofs for previous bounds. Methods developed in a result about one letter alphabets are extended to get a complete characterization for the problem of deciding if one input-expression describes a given language. The complexity depends only on the property of the given language to be finite, infinite but bounded, or unbounded.
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References
Aho, A.V., J.E. Hopcroft and J.D. Ullman, "The Design and Analysis of Computer Algorithms", Addison-Wesley, Reading, Mass., 1974.
Chandra, A.K. and L.J. Stockmeyer, "Alternation", Proc. 17th Annual IEEE Symposium on Foundations of Comp. Sci., 98–108, 1976.
Fürer, M., "Non-elementary lower bounds in automata theory", (in German), Diss. ETH 6122 (Ph.D. Thesis), Zürich, 1978.
Hopcroft, J.E., W.J. Paul and L.G. Valiant, "On Time Versus Space", Journal of the Association for Computing Machinery 24, 332–337, 1977.
Hunt III, H.B., "The equivalence problem for regular expressions with intersection is not polynomial in tape", Tech. Report TR 73-161, Dept. of Computer Science, Cornell University, 1973.
Hunt III, H.B., D.J. Rosenkrantz and T.G. Szymanski, "On the Equivalence, Containment, and Covering Problems for the Regular and Context-Free Languages", J. of Computer and System Sciences 12, 222–268, 1976.
Kozen, D., "On parallelism in Turing machines", Proc. 17th Annual IEEE Symposium on Foundations of Comp. Sci., 89–97, 1976.
Meyer, A.R. and L.J. Stockmeyer, "The equivalence problem for regular expressions with squaring requires exponential space", Proc. 13th Annual IEEE Symposium on Switching and Automata Theory, 125–129, 1972.
Rangel, J.L. "The Equivalence Problem for Regular Expressions over One Letter is Elementary", 15th Annual Symposium on Switching and Automata Theory, 24–27, 1974.
Sieferas, J.I., M.J. Fischer and A.R. Meyer, "Refinements of the Nondeterministic Time and Space Hierarchies", Proc. 14th Annual IEEE Symposium on Switching and Automata Theory, 130–137, 1973.
Stockmeyer, L.J., "The complexity of decision problems in automata theory and logic". Report TR-133, M.I.T., Project MAC, Cambridge, Mass., 1974.
Stockmeyer, L.J. and A.R. Meyer, "Word Problems Requiring Exponential Time: Preliminary Report", Proc. 5th Annual ACM Symposium on the Theory of Computing, 1–9, 1973.
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Fürer, M. (1980). The complexity of the inequivalence problem for regular expressions with intersection. In: de Bakker, J., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 1980. Lecture Notes in Computer Science, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10003-2_74
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DOI: https://doi.org/10.1007/3-540-10003-2_74
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