Abstract
We study the Shannon information rate of accepting runs of various forms of automata. The rate is therefore a complexity indicator for executions of the automata. Accepting runs of finite automata and reversal-bounded nondeterministic counter machines, as well as their restrictions and variations, are investigated and are shown, in many cases, with computable execution rates. We also conduct experiments on C programs showing that estimating information rates for their executions is feasible in many cases.
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References
Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)
Asarin, E., Degorre, A.: Volume and Entropy of Regular Timed Languages: Discretization Approach. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 69–83. Springer, Heidelberg (2009)
Chhabra, J.K., Aggarwal, K.K., Singh, Y.: Code and data spatial complexity: two important software understandability measures. Information and Software Technology 45(8), 539–546 (2003)
Chhabra, J.K., Gupta, V.: Evaluation of object-oriented spatial complexity measures. SIGSOFT Softw. Eng. Notes 34(3), 1–5 (2009)
Chomsky, N., Miller, G.A.: Finite state languages. Information and Control 1, 91–112 (1958)
Cover, T.M., Thomas, J.A.: Elements of information theory, 2nd edn. Wiley-Interscience (2006)
Cui, C., Dang, Z., Ibarra, O.H., Fischer, T.R.: Information rate of some classes of non-regular languages: An automata-theoretic approach (2012) (submitted)
Dang, Z., Ibarra, O.H., Bultan, T., Kemmerer, R.A., Su, J.: Binary Reachability Analysis of Discrete Pushdown Timed Automata. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 69–84. Springer, Heidelberg (2000)
Dang, Z.: Pushdown timed automata: a binary reachability characterization and safety verification. Theor. Comput. Sci. 302(1-3), 93–121 (2003)
Douce, C.R., Layzell, P.J., Buckley, J.: Spatial measures of software complexity. In: Proc. 11th Meeting of Psychology of Programming Interest Group, Leeds (1999)
Halstead, M.H.: Elements of Software Science (Operating and programming systems series). Elsevier Science Inc. (1977)
Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation, 3rd edn. Addison-Wesley (2007)
Ibarra, O.H.: Reversal-bounded multicounter machines and their decision problems. Journal of the ACM 25(1), 116–133 (1978)
Ibarra, O.H., Dang, Z., Egecioglu, O., Saxena, G.: Characterizations of Catalytic Membrane Computing Systems. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 480–489. Springer, Heidelberg (2003)
Kuich, W.: On the entropy of context-free languages. Information and Control 16(2), 173–200 (1970)
Paun, G.: Membrane Computing, An Introduction. Springer (2002)
Shannon, C.E., Weaver, W.: The Mathematical Theory of Communication. University of Illinois Press (1949)
Shao, J., Wang, Y.: A new measure of software complexity based on cognitive weight. Can. J. Elect. Comput. Eng. 28(2), 69–74 (2003)
Staiger, L.: The Entropy of Lukasiewicz-Languages. In: Kuich, W., Rozenberg, G., Salomaa, A. (eds.) DLT 2001. LNCS, vol. 2295, pp. 155–165. Springer, Heidelberg (2002)
Xie, G., Dang, Z., Ibarra, O.H.: A Solvable Class of Quadratic Diophantine Equations with Applications to Verification of Infinite State Systems. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 668–680. Springer, Heidelberg (2003)
Yang, L., Cui, C., Dang, Z., Fischer, T.R.: An information-theoretic complexity metric for labeled graphs (2011) (in review)
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Cui, C., Dang, Z., Fischer, T.R., Ibarra, O.H. (2013). Execution Information Rate for Some Classes of Automata. In: Dediu, AH., MartÃn-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2013. Lecture Notes in Computer Science, vol 7810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37064-9_21
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DOI: https://doi.org/10.1007/978-3-642-37064-9_21
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