Abstract
The chop or fusion operation was recently introduced in [S. A. Babu, P. K. Pandya: Chop Expressions and Discrete Duration Calculus. Modern Applications of Automata Theory, World Scientific, 2010], where a characterization of regular languages in terms of chop expressions was shown. Simply speaking, the chop or fusion of two words is a concatenation were the touching letters are coalesced, if both letters are equal; otherwise the operation is undefined. We investigate the descriptional complexity of the chop operation and its iteration for deterministic and nondeterministic finite automata as well as for regular expressions. In most cases tight bounds are shown. Moreover, we also consider the conversion problem between finite automata, regular expressions, and chop expressions. Again, for most conversions we get tight bounds in order of magnitude. It is worth mentioning that regular expressions can be transformed into equivalent chop expressions of polynomial size, but chop expressions can be exponentially more succinct than regular expressions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Babu, S.A., Pandya, P.K.: Chop expressions and discrete duration calculus. In: D’Souza, D., Shankar, P. (eds.) Modern Applications of Automata Theory. IISc research Monographs Series, vol. 2. World Scientific, Singapore (2010)
Birget, J.-C.: Intersection and union of regular languages and state complexity. Inform. Process. Lett. 43, 185–190 (1992)
Brzozowski, J.A., McCluskey, E.J.: Signal flow graph techniques for sequential circuit state diagrams. IEEE Trans. Comput. C-12(2), 67–76 (1963)
Cărăuşu, A., Păun, G.: String intersection and short concatenation. Rev. Roumaine Math. Pures Appl. 26, 713–726 (1981)
Cohen, R.S.: Star height of certain families of regular events. J. Comput. System Sci. 4(3), 281–297 (1970)
Domaratzki, M.: Minimality in Template-Guided Recombination. Inform. and Comput. 207, 1209–1220 (2009)
Harel, D., Peleg, D.: Process logic with regular formulas. Theoret. Comput. Sci. 38, 307–322 (1985)
Ehrenfeucht, A., Zeiger, H.P.: Complexity measures for regular expressions. J. Comput. System Sci. 12(2), 134–146 (1976)
Gelade, W., Neven, F.: Succinctness of complement and intersection of regular expressions. In: STACS, Bordeaux, France, pp. 325–336. Schloss Dagstuhl–Leibniz-Zentrum für Informatik, Dagstuhl (2008)
Glushkov, V.M.: The abstract theory of automata. Russian Math. Surveys 16, 1–53 (1961)
Gruber, H., Holzer, M.: Finite automata, digraph connectivity, and regular expression size. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 39–50. Springer, Heidelberg (2008)
Gruber, H., Holzer, M.: Language operations with regular expressions of polynomial size. Theoret. Comput. Sci. 410(35), 3281–3289 (2009)
Hashiguchi, K.: Algorithms for determining the relative star height and star height. Inform. Comput. 78(2), 124–169 (1988)
Hashiguchi, K., Honda, N.: Homomorphisms that preserve star height. Inform. Comput. 30(3), 247–266 (1976)
Holzer, M., Jakobi, S.: State complexity of chop operations on unary and finite languages (2011) (in preparation)
Holzer, M., Jakobi, S., Kutrib, M.: The chop of languages. In: AFL, Debrecen, Hungary (to appear, 2011)
Holzer, M., Kutrib, M.: Nondeterministic descriptional complexity of regular languages. Internat. J. Found. Comput. Sci. 14(6), 1087–1102 (2003)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading (1979)
Ito, M., Lischke, G.: Generalized periodicity and primitivity. Math Logic Q 53, 91–106 (2007)
Kallas, J., Kufleitner, M., Lauser, A.: First-order fragments with successor over infinite words. In: STACS, Dortmund, Germany, pp. 356–367. Schloss Dagstuhl–Leibniz-Zentrum für Informatik, Dagstuhl (2011)
Maslov, A.N.: Estimates of the number of states of finite automata. Soviet Math. Dokl. 11, 1373–1375 (1970)
Mateescu, A., Salomaa, A.: Parallel composition of words with re-entrant symbols. An. Univ. Bucuresti, Mat.-Inform. 45, 71–80 (1996)
Meyer, A.R., Fischer, M.J.: Economy of description by automata, grammars, and formal systems. In: SWAT, pp. 188–191. IEEE Computer Society Press, Los Alamitos (1971)
Moore, F.R.: 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, 1211–1219 (1971)
Rabin, M.O., Scott, D.: Finite automata and their decision problems. IBM J. Res. Dev. 3, 114–125 (1959)
Rich, E.A.: Automata, Computability, and Complexity: Theory and Applications. Prentice Hall, Englewood Cliffs (2007)
Sakarovitch, J.: The language, the expression, and the (small) automaton. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, pp. 15–30. Springer, Heidelberg (2006)
Thompson, K.: Regular expression search algorithm. Com. ACM 11(6), 419–422 (1968)
Yu, S.: State complexity of regular languages. J. Autom. Lang. Comb. 6, 221–234 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Holzer, M., Jakobi, S. (2011). Chop Operations and Expressions: Descriptional Complexity Considerations. 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_23
Download citation
DOI: https://doi.org/10.1007/978-3-642-22321-1_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22320-4
Online ISBN: 978-3-642-22321-1
eBook Packages: Computer ScienceComputer Science (R0)