Abstract
Deterministic two-way finite state transductions are exactly the mso definable string transductions. Nondeterministic mso definable string transductions equal compositions of nondeterministic two-way finite state transductions that have the finite visit property. Both families of mso definable string transductions are characterized in terms of Hennie machines.
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
J.-C. Birget, Two-way automata and length-preserving homomorphisms, MST 29 (1996) 191–226.
J.R. Büchi, Weak second-order arithmetic and finite automata, Zeitschrift für Mathematik, Logik und Grundlagen der Mathematik 6 (1960) 66–92.
M.P. Chytil, V. Jákl, Serial composition of 2-way finite-state transducers and simple programs on strings, in: 4th ICALP, LNCS vol. 52, Springer Verlag, 1977, pp. 135–147.
B. Courcelle, The monadic second-order logic of graphs V: on closing the gap between definability and recognizability, TCS 80 (1991) 153–202.
B. Courcelle, Monadic second-order definable graph transductions: a survey, TCS 126 (1994) 53–75.
B. Courcelle, The expression of graph properties and graph transformations in monadic second-order logic, in: Handbook of graph grammars and computing by graph transformation vol. 1 (G. Rozenberg, ed.), World Scientific Publishing Co., 1997, pp. 313–400.
J. Engelfriet, Three hierarchies of transducers, MST 15 (1982) 95–125.
J. Engelfriet, Context-free graph grammars, in: A. Salomaa (eds.), Handbook of Formal Languages, vol. 3: Beyond Words, Springer Verlag, 1997 [17]}, pp. 125–213.
J. Engelfriet, V. van Oostrom, Logical description of context-free graph-languages, JCSS 55 (1997) 489–503.
S.A. Greibach, Visits, crosses, and reversals for nondeterministic off-line machines, Inf. Control 36 (1978) 174–216.
S.A. Greibach, One way finite visit automata, TCS 6 (1978) 175–221.
S.A. Greibach, Hierarchy theorems for two-way finite state transducers, Acta Inf. 11 (1978) 89–101.
F.C. Hennie, One-tape, off-line Turing machine computations, Inf. Control 8 (1965) 553–578.
J.E. Hopcroft, J.D. Ullman, An approach to a unified theory of automata, The Bell System Technical Journal 46 (1967) 1793–1829.
D. Kiel, Two-way a-transducers and AFL, JCSS 10 (1975) 88–109.
V. Rajlich, Bounded-crossing transducers, Inf. Control 27 (1975) 329–335.
G. Rozenberg, A. Salomaa (eds.), Handbook of Formal Languages, vol. 3: Beyond Words, Springer Verlag, 1997.
D. Seese, Interpretability and tree automata: a simple way to solve algorithmic problems on graphs closely related to trees, in: Tree Automata and Languages (M. Nivat, A. Podelski, eds.), Elsevier Science Publishers, 1992, pp. 83–114.
W. Thomas, Languages, automata, and logic, in: A. Salomaa (eds.), Handbook of Formal Languages, vol. 3: Beyond Words, Springer Verlag, 1997 [17]}, pp. 389–455.
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
Engelfriet, J., Hoogeboom, H.J. (1999). Two-way finite state transducers and monadic second-order logic. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_28
Download citation
DOI: https://doi.org/10.1007/3-540-48523-6_28
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66224-2
Online ISBN: 978-3-540-48523-0
eBook Packages: Springer Book Archive