Abstract
We consider the problem of computing the least solution X i , i=1,..., n, of a system of equations x i=f i, i=1,..., n, over N, i.e., the naturals (extended by ∞), where the right hand sides f i are expressions built up from constants and variables by operations taken from some set Ω. We present efficient algorithms for various subsets Ω of the operations minimum, maximum, addition and multiplication.
Preview
Unable to display preview. Download preview PDF.
References
B. Courcelle, M. Mosbah: Monadic Second-Order Evaluations on Tree-Decomposable Graphs. Theor. Comp. Sci. 109 (1993), 49–82
P. Cousot, R. Cousot: Abstract Interpretation: A Unified Lattice Model for Static Analysis of Programs by Construction or Approximation of Fixpoints. 4th Symp. on Principles of Programming Languages, 238–252, Los Angeles, California, 1977
P. Cousot, R. Cousot: Comparing the Galois Connection and Widening/Narrowing Approaches to Abstract Interpretation. Tech. Report LIENS 92-16, Paris, 1992
P. Cousot, R. Cousot: Abstract Interpretation and Application to Logic Programs. Tech. Report LIX/RR/92/08, Palaiseau, 1992
M.L. Fredman, R.E. Tarjan: Fibonacci Heaps and Their Uses in Improved Network Optimization Algorithms. JACM (34), 597–615, 1987
A. Habel, H.-J. Kreowski, W. Vogler: Decidable Boundedness Problems for Sets of Graphs Generated by Hyperedge-Replacement. Theor. Comp. Sci. 89 (1991), 33–62
C. Hankin, S. Hunt: Fixed Points and Frontiers: A New Perspective. J. of Functional Programming (1), 91–120, 1991
K. Kennedy: A Survey of Data Flow Analysis Techniques. In: S.S. Muchnick, N.D. Jones (eds.): Program Flow Analysis. Theory and Applications. Prentice-Hall, 1981
T.J. Marlowe, B.G. Ryder: Properties of Data Flow Frameworks. Acta Informatica (28), 121–163, 1990
F. Nielson, H.R. Nielson: Bounded Fixed Point Iteration. J. Logic Computat. (2), 441–464, 1992
F. Nielson, H.R. Nielson: Finiteness Conditions for Fixed Point Iteration. Prog. of LISP and Functional Programming 1992, 96–108
S. Peyton-Jones, C. Clack: Finding Fixpoints in Abstract Interpretations. In: S. Abramsky, C. Hankin (Eds.): Abstract Interpretation of Declarative Languages, 246–265 Ellis Horwood Ltd. and John Wiley, 1987
H. Seidl: Tree Automata with Cost Functions. Proc. CAAP'92, LNCS 581, 279–299, 1992; long version to appear in TCS, special issue on CAAP'92
H. Seidl: Equality of Instances of Variables in FORK. Tech. Rep. 6/93, SFB 124–C1, Saarbrücken, 1993
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Seidl, H. (1994). Least solutions of equations over N . In: Abiteboul, S., Shamir, E. (eds) Automata, Languages and Programming. ICALP 1994. Lecture Notes in Computer Science, vol 820. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58201-0_85
Download citation
DOI: https://doi.org/10.1007/3-540-58201-0_85
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58201-4
Online ISBN: 978-3-540-48566-7
eBook Packages: Springer Book Archive