A Free Energy Foundation of Semantic Similarity in Automata and Languages

Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9939)

Abstract

This paper develops a free energy theory from physics including the variational principles for automata and languages and also provides algorithms to compute the energy as well as efficient algorithms for estimating the nondeterminism in a nondeterministic finite automaton. This theory is then used as a foundation to define a semantic similarity metric for automata and languages. Since automata are a fundamental model for all modern programs while languages are a fundamental model for the programs’ behaviors, we believe that the theory and the metric developed in this paper can be further used for real-word programs as well.

Keywords

Free Energy Periodic Orbit Semantic Similarity Regular Language Finite Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

We would like to thank Jean-Charles Delvenne, David Koslicki, Daniel J. Thompson, Eric Wang, William J. Hutton III, and Ali Saberi for discussions. We would also like to thank the seven referees for suggestions and comments that have improved the presentation of our results.

References

  1. 1.
    Chartrand, G., Kubicki, G., Schultz, M.: Graph similarity, distance in graphs. Aequationes Math. 55(1), 129–145 (1998)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Chomsky, N., Miller, G.A.: Finite state languages. Inf. Control 1(2), 91–112 (1958)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Cui, C., Dang, Z., Fischer, T.R.: Typical paths of a graph. Fundam. Inform. 110( 1–4), 95–109 (2011)MathSciNetMATHGoogle Scholar
  4. 4.
    Cui, C., Dang, Z., Fischer, T.R., Ibarra, O.H.: Similarity in languages and programs. Theor. Comput. Sci. 498, 58–75 (2013)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Cui, C., Dang, Z., Fischer, T.R., Ibarra, O.H.: Information rate of some classes of non-regular languages: an automata-theoretic approach. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds.) MFCS 2014. LNCS, vol. 8634, pp. 232–243. Springer, Heidelberg (2014)Google Scholar
  6. 6.
    Cui, C., Dang, Z., Fischer, T.R., Ibarra, O.H.: Execution information rate for some classes of automata. Inf. Comput. 246, 20–29 (2016)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Dang, Z., Dementyev, D., Fischer, T.R., Hutton III, W.J.: Security of numerical sensors in automata. In: Drewes, F. (ed.) CIAA 2015. LNCS, vol. 9223, pp. 76–88. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  8. 8.
    Dehmer, M., Emmert-Streib, F., Kilian, J.: A similarity measure for graphs with low computational complexity. Appl. Math. Comput. 182(1), 447–459 (2006)MathSciNetMATHGoogle Scholar
  9. 9.
    Delvenne, J.-C., Libert, A.-S.: Centrality measures and thermodynamic formalism for complex networks. Phys. Rev. E 83, 046117 (2011)CrossRefGoogle Scholar
  10. 10.
    ElGhawalby, H., Hancock, E.R.: Measuring graph similarity using spectral geometry. In: Campilho, A., Kamel, M.S. (eds.) ICIAR 2008. LNCS, vol. 5112, pp. 517–526. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  11. 11.
    Gurevich, B.M.: A variational characterization of one-dimensional countable state gibbs random fields. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 68(2), 205–242 (1984)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Harel, D.: Statecharts: a visual formalism for complex systems. Sci. Comput. Program. 8(3), 231–274 (1987)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Ibarra, O.H., Cui, C., Dang, Z., Fischer, T.R.: Lossiness of communication channels modeled by transducers. In: Beckmann, A., Csuhaj-Varjú, E., Meer, K. (eds.) CiE 2014. LNCS, vol. 8493, pp. 224–233. Springer, Heidelberg (2014)Google Scholar
  14. 14.
    Koslicki, D.: Topological entropy of DNA sequences. Bioinformatics 27(8), 1061–1067 (2011)CrossRefGoogle Scholar
  15. 15.
    Koslicki, D., Thompson, D.J.: Coding sequence density estimation via topological pressure. J. Math. Biol. 70(1), 45–69 (2014)MathSciNetMATHGoogle Scholar
  16. 16.
    Li, Q., Dang, Z.: Sampling automata and programs. Theor. Comput. Sci. 577, 125–140 (2015)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Naval, S., Laxmi, V., Rajarajan, M., Gaur, M.S., Conti, M.: Employing program semantics for malware detection. IEEE Trans. Inf. Forensics Secur. 10(12), 2591–2604 (2015)CrossRefGoogle Scholar
  18. 18.
    Ruelle, D.: Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics. Cambridge University Press/Cambridge Mathematical Library, Cambridge (2004)CrossRefMATHGoogle Scholar
  19. 19.
    Sarig, O.M.: Thermodynamic formalism for countable Markov shifts. Ergodic Theor. Dyn. Syst. 19, 1565–1593 (1999)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Sarig, O.M.: Lecture notes on thermodynamic formalism for topological Markov shifts (2009)Google Scholar
  21. 21.
    Shannon, C.E., Weaver, W.: The Mathematical Theory of Communication. University of Illinois Press, Urbana (1949)MATHGoogle Scholar
  22. 22.
    Sokolsky, O., Kannan, S., Lee, I.: Simulation-based graph similarity. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 426–440. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  23. 23.
    Walters, P.: An Introduction to Ergodic Theory. Graduate Texts in Mathematics. Springer, New York (1982)CrossRefMATHGoogle Scholar
  24. 24.
    Zager, L.A., Verghese, G.C.: Graph Similarity Scoring and Matching. Appl. Math. Lett. 21(1), 86–94 (2008)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.School of Electrical Engineering and Computer ScienceWashington State UniversityPullmanUSA

Personalised recommendations