Abstract
Since Muller and Schupp have shown that monadic second-order logic is decidable for context-free graphs in [MS85], several specialized procedures have been developed for related problems, mostly for sublogics like the modal μ-calculus, or even its alternation-free fragment. This work shows the decidability of SlS, the trace version of MSOL, for the richer set of macro graphs. The generation mechanism of macro graphs is of higher-order nature and relates to the context-free one like macro grammars [Fis68] relate to context-free grammars.
Technically, the result follows from the decidability of the emptiness problem of the trace language of a macro graph with fairness. The decision procedure is given in form of a tableau system. Soundness and completeness follow from the relation of the (finite) tableaux to their infinite unfoldings. This kind of proof promises to be helpful in the derivation of further results.
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. Bouajjani, R. Echahed, and P. Habermehl, Verifying infinite state processes with sequential and parallel composition, 22nd ACM Symp. on Principles of Programming Languages, 1995.
O. Burkart and Y.-M. Quemener, Model-checking of infinite graphs defined by graph grammars, Infinity 96, ENTCS 6, Elsevier, 1996.
Olaf Burkart and Bernhard Steffen, Model checking for context-free processes, 3rd Int. Conf. on Concurrency Theory (R. Cleaveland, ed.), LNCS 630, Springer, 1992, pp. 123–137.
Olaf Burkart and Bernhard Steffen, Pushdown processes: Parallel composition and model checking, 5th Int. Conf. on Concurrency Theory (B. Jonsson and J. Parrow, eds.), LNCS 836, Springer, 1994, pp. 98–113.
Olaf Burkart and Bernhard Steffen, Model checking the full mu-calculus for infinite sequential processes, 24th Int. Coll. on Automata, Languages and Programming (Degano, Gorrieri, and Marchetti-Spaccamela, eds.), LNCS 1256, Springer, 1997, pp. 419–429.
W. Damm, An algebraic extension of the Chomsky-hierarchy, 8th Conf. on Math. Found. of Comp. Sc. (J. Bečvář, ed.), LNCS 74, 1979, pp. 266–276.
M.J. Fischer, Grammars with macro-like productions, 9th Conf. on Switching and Automata Theory, IEEE, 1968, pp. 131–142.
A. Habel, Hyperedge replacement: Grammars and languages, LNCS 643, Springer, 1992.
H. Hungar, Model checking of macro processes, 6th Int. Conf. on Computer Aided Verification (D.L. Dill, ed.), LNCS 818, Springer, 1994, pp. 169–181.
Hardi Hungar, Beyond finite-state model checking: Verifying large and infinite systems, Habilitation, CvO University Oldenburg, 1998.
A.J. Kfoury, J. Tiuryn, and P. Urzyczyn, The hierarchie of finitely typed functional programs, 2nd IEEE Symp. on Logic in Comp. Sc, 1987, pp. 225–235.
D.E. Muller and P.E. Schupp, The theory of ends, pushdown automata, and second-order logic, Theor. Comp. Sc. 37 (1985), 51–75.
Wolfgang Thomas, Automata on infinite objects, Handbook of Theoretical Computer Science (J. van Leeuwen, ed.), Elsevier, 1990.
I. Walukiewicz, Pushdown processes: games and model-checking, 8th Int. Conf. on Computer Aided Verification, LNCS 1102, Springer, 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hungar, H. (1999). Model Checking and Higher-Order Recursion. In: Kutyłowski, M., Pacholski, L., Wierzbicki, T. (eds) Mathematical Foundations of Computer Science 1999. MFCS 1999. Lecture Notes in Computer Science, vol 1672. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48340-3_14
Download citation
DOI: https://doi.org/10.1007/3-540-48340-3_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66408-6
Online ISBN: 978-3-540-48340-3
eBook Packages: Springer Book Archive