Abstract
In this paper, we study modular aspects of hierarchical and super hierarchical combinations of term rewriting systems. In particular, a sufficient condition for modularity of semi-completeness of hierarchical and super hierarchical combinations is proposed. We first establish modularity of weak normalization for this class (defined by the sufficient condition) and modularity of semi-completeness for a class of crosswise independent unions. From these results, we obtain modularity of semi-completeness for a class of hierarchical and super hierarchical combinations. Our results generalize the semi-completeness results of Ohlebusch [14] and Middeldorp and Toyama [13]. The notion of crosswise independent unions is a generalization of both constructor sharing unions as well as Plump's crosswise disjoint unions.
Some of the details were worked out during the author's stay at Max-Planck-Institut für Informatik, Saarbrücken.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
N. Dershowitz and J.-P. Jouannaud (1990), Rewrite Systems, In J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, Vol. B, pp. 243–320, North-Holland.
N. Dershowitz (1995), Hierarchical termination, to appear in Proc. of CTRS'94, forthcoming LNCS, Springer-Verlag.
B. Gramlich (1992), Relating innermost, weak, uniform and modular termination of term rewrite systems, Proc. of Logic Prog. and Automated Reasoning, LPAR'92, Lecture Notes in Computer Science 624, pp. 285–296, Springer-Verlag.
B. Gramlich (1994), Generalized sufficient conditions for modular termination of rewriting, in AAECC (Applicable Algebra in Engineering, Communication and Computing) 5, pp. 131–158.
J.W. Klop (1992), Term Rewriting Systems, tech rep. CS-R9073, CWI, Amsterdam. Also appears as a chapter in S. Abramsky, D. Gabbay and T. Maibaum (ed.), Handbook of Logic in Computer Science, Vol. 2, Oxford University Press.
M.R.K. Krishna Rao (1993), Completeness of hierarchical combinations of term rewriting systems, Proc. of 13th conference on Foundations of Software Technology and Theoretical Computer Science, FST&TCS'93, Lecture Notes in Computer Science 761, pp. 125–138, Springer-Verlag.
M.R.K. Krishna Rao (1994), Simple termination of hierarchical combinations of term rewriting systems, Proc. of Theoretical Aspects of Computer Science, TACS'94, Lecture Notes in Computer Science 789, pp. 203–223, Springer-Verlag.
M.R.K. Krishna Rao (1994), Semi-completeness of hierarchical and super hierarchical combinations of term rewriting systems, Technical report, TIFR, Bombay, October.
M. Kurihara and A. Ohuchi (1990), Modularity of simple termination of term rewriting systems, Journal of IPS, Japan 34, pp. 632–642.
M. Kurihara and A. Ohuchi (1992), Modularity of simple termination of term rewriting systems with shared constructors, Theoretical Computer Science 103, pp. 273–282.
A. Middeldorp (1989), A sufficient condition for the termination of the direct sum of terra rewriting systems, Proc. of LICS'89, pp. 396–401.
A. Middeldorp (1990), Modular properties of term rewriting systems, Ph.D. Thesis, Free University, Amsterdam.
A. Middeldorp and Y. Toyama (1991), Completeness of combinations of constructor systems, Proc. of RTA'91, Lecture Notes in Computer Science 488, pp. 188–199, Springer-Verlag. Also appears in J. Symb. Comp. 15, pp. 331–348.
E. Ohlebusch (1994), On the modularity of confluence of constructor-sharing term rewriting systems, Proc. of CAAP'94, Lecture Notes in Computer Science 787, pp.261–275, Springer-Verlag.
D. Plump (1993), Evaluation of functional expressions by hypergraph rewriting, Ph.D. Thesis, University of Bremen.
M. Rusinowitch (1987), On termination of the direct sum of term rewriting systems, Information Processing Letters, IPL 26, pp. 65–70.
J. Staples (1975), Church-Roser Theorems for Replacement Systems, in J. Crosley (ed.), Algebra and Logic, Lecture Notes in Mathematics, Vol 450, pp. 291–307, Springer-Verlag.
Y. Toyama (1987), On the Church-Rosser property for the direct sum of term rewriting systems, JACM 34, pp. 128–143.
Y. Toyama (1987), Counterexamples to termination for the direct sum of term rewriting systems, Information Processing Letters, IPL 25, pp. 141–143.
Y. Toyama, J.W. Klop and H.P. Barendrget (1989), Termination for the direct sum of left-linear term rewriting systems, Proc. of RTA'89, Lecture Notes in Computer Science 355, pp. 477–491, Springer-Verlag.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rao, M.R.K.K. (1995). Semi-completeness of hierarchical and super-hierarchical combinations of term rewriting systems. In: Mosses, P.D., Nielsen, M., Schwartzbach, M.I. (eds) TAPSOFT '95: Theory and Practice of Software Development. CAAP 1995. Lecture Notes in Computer Science, vol 915. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59293-8_208
Download citation
DOI: https://doi.org/10.1007/3-540-59293-8_208
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-59293-8
Online ISBN: 978-3-540-49233-7
eBook Packages: Springer Book Archive