Abstract
We implement a set of procedures for deciding whether or not a language given by its minimal automaton or by its syntactic semigroup is locally testable, right or left locally testable, threshold locally testable, strictly locally testable, or piecewise testable. The bounds on order of local testability of transition graph and order of local testability of transition semigroup are also found. For given k, the k-testability of transition graph is verified. Some new effective polynomial time algorithms are used. These algorithms have been implemented as a C/C++ package.
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
D. Beauquier, J.E. Pin, Factors of words, Lect. Notes in Comp. Sci., 372(1989), 63–79.
J.A. Brzozowski, I. Simon, Characterizations of locally testable events, Discrete Math. 4(1973), 243–271.
P. Caron, LANGAGE: A Maple package for automaton characterization of regular languages, Springer, Lect. Notes in Comp. Sci., 1436(1998), 46–55.
P. Caron, Families of locally testable languages, Theoret. Comput. Sci., 242(2000), 361–376.
J.M. Camparnaud, G. Hansel, Automate, a computing package for automata and finite semigroups, J. of Symbolic Comput., 12(1991), 197–220.
G. Cousineau, J.F. Perrot, J.M. Rifflet, APL programs for direct computation of a finite semigroup, APL Congress 73, Amsterdam, North Holl. Publ., (1973) 67–74.
V. Froidure, J.-E. Pin, Algorithms for computing finite semigroups. F. Cucker and M. Shub eds., Foundations of Comp. Math. (1997), 112–126.
P. Garcia, Jose Ruiz, Right and left locally testable languages, Theoret. Comput. Sci., 246(2000), 253–264.
S. Kim, R. McNaughton, R. McCloskey, A polynomial time algorithm for the local testability problem of deterministic finite automata, IEEE Trans. Comput., N10, 40(1991) 1087–1093.
S. Kim, R. McNaughton, Computing the order of a locally testable automaton, Lect. Notes in Comp. Sci., 560(1991) 186–211.
R. König, Reduction algorithm for some classes of aperiodic monoids, R.A.I.R.O. Theor.Inform., 19, 3(1985), 233–260.
E. Leiss, Regpack, an interactive package for regular languages and finite automata, Research report CS-77-32, Univ. of Waterloo, 1977.
O. Matz, A. Miller, A. Pottho., W. Thomas, E. Valkema, Report on the program AMoRE, Inst. inf. und pract. math., Christian-Albrecht Univ. Kiel, 1995.
R. McNaughton, Algebraic decision procedure for local testability, Math. Syst. Theory, 8( 1974), 60–76.
R. McNaughton, S. Papert, Counter-free automata, M.I.T. Press Mass., (1971).
A. Okhotin, Whale Calf, a parser generator for conjunctive grammars. 7-th Int. Conf. on Impl. and Appl. of Automata, CIAA2002, Tours, 2002, 211–216.
D. Raymond, D. Wood, Grail, a C++ library for automata and expressions, J. of Symb. Comp., 17(1994) 341–350.
I. Simon, Piecewise testable events, Lect. Notes in Comp. Sci., 33(1975), 214–222.
J. Stern, Complexity of some problems from the theory of automata. Inf. and Control, 66(1985), 163–176.
K. Sutner, Finite State Mashines and Syntactic Semigroups, The Mathematica J., 2(1991), 78–87.
A.N. Trahtman, The varieties of testable semigroups. Semigroup Forum, 27, (1983), 309–318.
A.N. Trahtman, A polynomial time algorithm for local testability and its level. Int. J. of Algebra and Comp., vol. 9, 1(1998), 31–39.
A.N. Trahtman, Identities of locally testable semigroups. Comm. in Algebra, v. 27, 11(1999), 5405–5412.
A.N. Trahtman, Algorithms finding the order of local testability of deterministic finite automaton and estimation of the order, Th. Comp. Sci., 235(2000), 183–204.
A.N. Trahtman, Piecewise and local threshold testability of DFA. Lect. Notes in Comp. Sci., 2138(2001), 347–358.
A.N. Trahtman, An algorithm to verify local threshold testability of deterministic finite automata. Lect. Notes in Comp. Sci., 2214(2001), 164–173.
B.W. Watson, The design and implementation of the FIRE Engine: A C++ toolkit for Finite Automata and Regular Expressions, Comp. Sci. Rep. 94722, Endhoven Univ. of Techn. 1994.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Trahtman, A.N. (2003). A Package TESTAS for Checking Some Kinds of Testability. In: Champarnaud, JM., Maurel, D. (eds) Implementation and Application of Automata. CIAA 2002. Lecture Notes in Computer Science, vol 2608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44977-9_22
Download citation
DOI: https://doi.org/10.1007/3-540-44977-9_22
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40391-3
Online ISBN: 978-3-540-44977-5
eBook Packages: Springer Book Archive