Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-19T02:59:38.606Z Has data issue: false hasContentIssue false
  • English
  • Français

A categorical look at tree automata and context-free languages

Published online by Cambridge University Press:  04 March 2009

Kimmo I. Rosenthal
Kimmo I. Rosenthal
Affiliation:
Union College, Department of Mathematics, Bailey Hall, Schenectady, New York
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article, we indicate how the category theoretical approach to tree automata, due to Betti and Kasangian, can be fruitfully combined with Walters’ categorical approach to context-free grammars to provide a simple way of establishing the well-known correspondence between context-free languages and the behaviors of non-deterministic tree automata. The connecting link between the two notions is provided by the theory of relational presheaves.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 4 , Issue 3 , September 1994 , pp. 287 - 293
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Betti, R. and Carboni, A. (1982) Cauchy completion and the associated sheaf. Cah. de Top. et Géom. Diff. XXIII (3) 243–256.Google Scholar
Betti, R. and Kasangian, S. (1985) Tree automata and enriched category theory. Rend. Istit. Mat. Univ. Trieste 17 (1–2) 71–78.Google Scholar
Gecseg, F. and Steinby, M. (1986) Tree Automata, Akademiai Kiado, Budapest.Google Scholar
Ghilardi, S. and Meloni, G. C. (1990) Modal logics with n-ary connectives. Zeitschr.f. Math. Logik und Grundlagen der Math. 36 193–215.CrossRefGoogle Scholar
Kasangian, S. and Rosebrugh, R. (1986) Decompositions of automata and enriched category theory. Cah. de Top. et Géom. Diff. Cat. XXVII (4) 137–143.Google Scholar
Lambek, J. (1989) Multicategories revisited. In: Gray, J. and Scedrov, A. (eds.) Categories in Computer Science and Logic. Cont. Math. 92, American Math. Soc. 217–240.Google Scholar
Lawvere, F. W. (1963) Functorial semantics of algebraic theories. Proc. Nat. Acad. Sci. USA 50 869–872.CrossRefGoogle ScholarPubMed
Rosenthal, K. I. (1991) Free quantaloids. J. Pure Appl. Alg. 72 (1) 67–82.CrossRefGoogle Scholar
Rosenthal, K. I. (1992) Quantaloidal nuclei, the syntactic congruence and tree automata. J. Pure Appl. Alg. 77 189–205.CrossRefGoogle Scholar
Rosenthal, K. I. (1993) The Theory of Quantaloids (manuscript).Google Scholar
Walters, R. F. C. (1989a) A note on context-free languages. J Pure Appl. Alg. 62 199–203.CrossRefGoogle Scholar
Walters, R. F. C. (1989b) The free category with products on a multigraph. J. Pure Appl. Alg. 62 205–210.CrossRefGoogle Scholar
Walters, R. F. C. (1992) Category Theory and Computer Science, Cambridge University Press.CrossRefGoogle Scholar