Abstract
A number of basic questions concerning the state complexity research are discussed, which include why many basic problems weren’t studied earlier, whether there is a general algorithm for state complexity, and whether there is a new approach in this area of research. The new concept of state complexity approximation is also discussed. We show that this new concept can be used to obtain good results when the exact state complexities are difficult to find.
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References
Almeida, M., Moreira, N., Reis, R.: Enumeration and generation with a string automata representation. Theoretical Computer Science 387(2), 93–102 (2007)
Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to algorithms. The MIT Press and McGraw-Hill, Massachusetts (1990)
Ellul, K.: Descriptional complexity measures of regular languages, Master’s Thesis, University of Waterloo, Ontario (2002)
Ésik, Z., Gao, Y., Liu, G., Yu, S.: Estimation of state complexity of combined operations. Theoretical Computer Science 410(35), 3272–3280 (2009)
Fujiwara, S., Bochmann, G.V., Khendek, F., Amalou, M., Ghedamsi, A.: Test development - based on finite state machine (FSM) models. IEEE Transactions on Software Engineering 17(6), 591–603 (1991)
Gao, Y., Salomaa, K., Yu, S.: The state complexity of two combined operations: star of catenation and star of reversal. Fundamenta Informaticae 83(1-2), 75–89 (2008)
Gao, Y., Yu, S.: State complexity approximation. In: Proceedings of Descriptional Complexity of Formal Systems, pp. 163–174 (2009)
Garey, M.R., Graham, R.L., Ullman, J.D.: Worst-case analysis of memory allocation algorithms. In: Proceedings of the 4th Annual ACM Symposium on the Theory of Computing, pp. 143–150 (1972)
Holzer, M., Kutrib, M.: Nondeterministic descriptional complexity of regular languages. International Journal of Foundations Computer Science 14, 1087–1102 (2003)
Holzer, M., Kutrib, M.: Unary language operations and their nondeterministic state complexity. In: Ito, M., Toyama, M. (eds.) DLT 2002. LNCS, vol. 2450, pp. 162–172. Springer, Heidelberg (2003)
Hopcroft, J.E., Ullman, J.D.: Introduction to automata theory, languages, and computation. Addison-Wesley, Reading (1979)
Johnson, D.S.: Fast allocation algorithms. In: Proceedings of the 13th Annual IEEE Symposium on Switching and Automata Theory, pp. 144–154 (1972)
Johnson, D.S.: Near-optimal bin packing algorithms, PhD Dissertation, Massachusetts Institute of Technology, Cambridge, MA (1993)
Kiraz, G.A.: Compressed storage of sparse finite-state transducers. In: Boldt, O., Jürgensen, H. (eds.) WIA 1999. LNCS, vol. 2214, p. 109. Springer, Heidelberg (2001)
Lupanov, O.B.: A comparison of two types of finite automata. Problemy Kibernetiki 9, 321–326 (1963) (in Russian)
Maslov, A.N.: Estimates of the number of states of finite automata. Dokl. Akad. Nauk SSSR 194, 1266–1268 (1970) (in Russian); English translation: Soviet Math. Dokl. 11, 1372–1375 (1970)
Moore, F.: On the bounds for state-set size in the proofs of equivalence between deterministic, nondeterministic, and two-way finite automata. IEEE Trans. Comput. C-20, 1211–1214 (1971)
Rozenberg, G., Salomaa, A.: Cornerstones of Undecidability. Prentice Hall, New York (1994)
Rumbaugh, J., Jacobson, I., Booch, G.: The United Modeling Language Reference Manual. Addison-Wesley, Reading (1999)
Salomaa, A.: Theory of automata. Pergamon Press, Oxford (1969)
Salomaa, A., Salomaa, K., Yu, S.: Undecidability of the state complexity of composed regular operations. In: Proceedings of LATA (2011) (to be published)
Salomaa, K., Yu, S.: Synchronization Expressions with Extended Join Operation. Theoretical Computer Science 207, 73–88 (1998)
Salomaa, A., Salomaa, K., Yu, S.: State complexity of combined operations. Theoretical Computer Science 383(2-3), 140–152 (2007)
Salomaa, K., Yu, S.: On the state complexity of combined operations and their estimation. International Journal of Foundations of Computer Science 18(4), 683–698 (2007)
Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of formal languages, vol. 1, pp. 41–110. Springer, New York (1997)
Yu, S., Zhuang, Q., Salomaa, K.: The state complexities of some basic operations on regular languages. Theoretical Computer Science 125(2), 315–328 (1994)
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Yu, S., Gao, Y. (2011). State Complexity Research and Approximation. In: Mauri, G., Leporati, A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22321-1_5
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DOI: https://doi.org/10.1007/978-3-642-22321-1_5
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