Abstract
This paper is concerned with the recognition problem for semi-extended regular expressions: given a semi-extended regular expression r of length m and an input string x of length n, determine if x ∈ L(r), where L(r) denotes the language denoted by r. Although the recognition algorithm based on nondeterministic finite automata (NFAs) for regular expressions is widely known, a similar algorithm based on finite automata is currently not known for semi-extended regular expressions. The existing algorithm is based on dynamic programming. We here present an efficient automata-based recognition algorithm by introducing a new model of alternating finite automata called partially input-synchronized alternating finite automata (PISAFAs for short). Our algorithm based on PISAFAs runs in O(mn 2) time and O(mn + kn 2) space, though the existing algorithm based on dynamic programming runs in O(mn 3) time and O(mn 2) space, where k is the number of intersection operators occurring in r. Thus our algorithm significantly improves the existing one.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A.V. Aho, Algorithms for finding patterns in strings, In J.V. Leeuwen, ed. Handbook of theoretical computer science, Elsevier Science Pub., 1990.
A.K. Chandra, D.C. Kozen and L.J. Stockmeyer, Alternation, J. Assoc. Comput. Mach. 28, 1, 114–133, 1981.
C.H. Chang, and R. Paige, From regular expressions to DFA’s using compressed NFA’s, Theoret. Comput. Sci., 178, 1–36, 1997.
J.R. Knight and E.W. Myers, Super-Pattern matching, Algorithmica, 13, 1-2, 211–243, 1995.
J. Dassow, J. Hromkovic, J. Karhuaki, B. Rovan and A. Slobodova, On the power of synchronization in parallel computation, In Proc. 14th MFCS’89, LNCS 379, 196–206, 1989.
J.E. Hopcroft and J.D. Ullman, Introduction to automata theory language and computation, Addison Wesley, Reading Mass, 1979.
J. Hromkovic, K. Inoue, B. Rovan, A. Slobodova, I. Takanami and K.W. Wagner, On the power of one-way synchronized alternating machines with small space, International Journal of Foundations of Computer Science, 3, 1, 65–79, 1992.
G. Myers, A four Russians algorithm for regular expression pattern matching, J. Assoc. Comput. Mach. 39, 4, 430–48, 1992.
A. Slobodova, On the power of communication in alternating machines, In Proc. 13th MFCS’88, LNCS 324, 518–528, 1988.
H. Yamamoto, On the power of input-synchronized alternating finite automata, Proc. COCOON’2000, LNCS, to appear.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yamamoto, H. (2000). An Automata-Based Recognition Algorithm for Semi-extended Regular Expressions. In: Nielsen, M., Rovan, B. (eds) Mathematical Foundations of Computer Science 2000. MFCS 2000. Lecture Notes in Computer Science, vol 1893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44612-5_65
Download citation
DOI: https://doi.org/10.1007/3-540-44612-5_65
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67901-1
Online ISBN: 978-3-540-44612-5
eBook Packages: Springer Book Archive