Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-15T02:46:59.225Z Has data issue: false hasContentIssue false
  • English
  • Français

On Distributive Fixed-Point Expressions

Published online by Cambridge University Press:  15 August 2002

Helmut Seidl and
Damian Niwiński
Helmut Seidl
Affiliation:
FB IV – Informatik, Universität Trier, 54286 Trier, Germany
Damian Niwiński
Affiliation:
Institute of Informatics, University of Warsaw, Ul. Banacha 2, 02-097 Warsaw, Poland
Get access

Abstract

For every fixed-point expression e of alternation-depth r,we construct a new fixed-point expression e' of alternation-depth 2 and size ${\cal O}(r\cdot|e|)$ . Expression e' is equivalent to e whenever operators are distributive and the underlyingcomplete lattice has a co-continuous least upper bound. We alternation-depth but also w.r.t. the increase in size of theresulting expression.

Keywords

Fixed-point expressionsdistributivityalternation-depthlowerbounds.

Information

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 33 , Issue 4-5 , July 1999, pp. 427 - 446
Copyright
© EDP Sciences, 1999

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.)

Article purchase

Temporarily unavailable

References

Andersen, H.R. and Vergauwen, B., Efficient Checking of Behavioral Relations and Modal Assertions Using Fixed-Point Inversion. In 7th International Conference on Computer-Aided Verification (CAV). Springer, Lecture Notes in Comput. Sci. 939 (1995) 142-154. CrossRef
A. Arnold, The µ-Calculus Alternation-Depth Hierarchy is Strict on Binary Trees. Theoret. Informatics. Appl., Special issue on FICS'98, to appear.
A. Arnold and D. Niwinski, Fixed Point Characterization of Weak Monadic Logic Definable Sets of Trees, M. Nivat and A. Podelski, Eds. Elsevier, Amsterdam, Tree Automata and Languages (1992) 159-188.
Bhat, G. and Cleaveland, R., Efficient Local Model Checking for Fragments of the Modal µ-Calculus. In Tools and Algorithms for the Construction and Analysis of Systems (TACAS). Springer, Lecture Notes in Comput. Sci. 1055 (1996) 107-126. CrossRef
Bradfield, J.C., Mu-Calculus Al, The Modalternation Hierarchy is Strict. In 7th International Conference on Concurrency Theory (CONCUR). Springer, Lecture Notes in Comput. Sci. 1119 (1986) 233-246. CrossRef
Doornbos, H., Backhouse, R. and van der Woude, J., Calculational Approach, A to Mathematical Induction. Theoret. Comput. Sci. 179 (1997) 103-135. CrossRef
Emerson, E.A., Jutla, C.S. and Sistla, A.P., Model-Checking, On for Fragments of µ-Calculus. In 5th International Conference on Computer-Aided Verification (CAV). Springer, Lecture Notes in Comput. Sci. 697 (1993) 385-396. CrossRef
Emerson, E.A. and Clarke, E.M., Characterizing Correctness Properties of Parallel Programs Using Fixpoints. In 7th International Colloquium on Automata, Languages and Programming (ICALP). Springer, Lecture Notes in Comput. Sci. 85 (1980) 169-181. CrossRef
L. Flon and N. Suzuki, Consistent and Complete Proof Rules for the Total Correctness of Parallel Programs. In 19th IEEE Symp. on Foundations of Computer Science (FOCS) (1978).
Jurdzinski, M., Deciding the Winnner in Parity Games is in UP ⋂ co-UP. Inform. Process. Lett. 68 (1998) 119-124. CrossRef
Lenzi, G., Hierarchy Theorem, A for the µ-Calculus. In 23rd International Colloquium on Automata, Languages and Programming (ICALP). Springer, Lecture Notes in Comput. Sci. 1099 (1996) 87-109. CrossRef
D.E. Muller, A. Saoudi and P.E. Schupp, Alternating Automata, the Weak Monadic Theory of the Tree and its Complexity. In ICALP'86 (1986).
Niwinski, D., Fixed Point Clones, On. In 13th International Colloquium on Automata, Languages and Programming (ICALP). Springer, Lecture Notes in Comput. Sci. 226 (1986) 464-473. CrossRef
D. Niwinski, Hierarchy of Objects Definable in the Fixed Point Calculus, in Polish . Ph.D. Thesis, University of Warsaw (1987).
D. Niwinski, Fixed Points vs. Infinite Generation. In 3rd Annual IEEE Symposium on Logic in Computer Science (LICS), IEEE (1988) 402-409.
Niwinski, D., Fixed Point Characterization of Infinite Behavior of Finite State Systems. Theoret. Comput. Sci. 189 (1997) 1-69. CrossRef
Park, D.M.R., On the Semantics of Fair Parallelism. In Abstract Software Specification. Springer, Lecture Notes in Comput. Sci. 86 (1980) 504-526. CrossRef
Park, D.M.R., Concurrency and Automata on Infinite Sequences. In Theoret. Comput. Sci. Springer, Lecture Notes in Comput. Sci. 104 (1981) 167-183. CrossRef
H. Rasiowa and R. Sikorski, Mathematics of Metamathematics. Panstowe Wydawnictwo Naukowe (1970).
W. Thomas, Automata on Infinite Objects, J. van Leeuwen, Ed., Handbook of Theoretical Computer Science. Elsevier, Amsterdam (1990).