TY - GEN

T1 - Proving termination with multiset orderings

AU - Dershowitz, Nachum

AU - Manna, Zohar

N1 - Publisher Copyright:
© 1979, Springer-Verlag Berlin Heidelberg. All Rights reserved.

PY - 1979

Y1 - 1979

N2 - A common tool for proving the termination of programs is the well-founded set, a set ordered in such a way as to admit no infinite descending sequences. The basic approach is to find a termination function that maps the values of the program variables into some well-founded set, such that the value of the termination function is continually reduced throughout the computation. All too often, the termination functions required are difficult to find and are of a complexity out of proportion to the program under consideration. However, by providing more sophisticated well-founded sets, the corresponding termination functions can be simplified. Given a well-founded set S, we consider ~Itisets over S, "sets" that admit multiple occurrences of elements taken from S. We define an ordering on all finite multisets over S that is induced by the given ordering on S. This multiset ordering is shown to be well-founded. The value of the multiset ordering is that it permits the use of relatively simple and intuitive termination functions in otherwise difficult termination proofs. In particular, we apply the multiset ordering to prove the termination of production systems, programs defined in terms of sets of rewriting rules. An extended version of this paper appeared as Memo AIM-310, Stanford Artificial Intelligence Laboratory, Stanford, California.

AB - A common tool for proving the termination of programs is the well-founded set, a set ordered in such a way as to admit no infinite descending sequences. The basic approach is to find a termination function that maps the values of the program variables into some well-founded set, such that the value of the termination function is continually reduced throughout the computation. All too often, the termination functions required are difficult to find and are of a complexity out of proportion to the program under consideration. However, by providing more sophisticated well-founded sets, the corresponding termination functions can be simplified. Given a well-founded set S, we consider ~Itisets over S, "sets" that admit multiple occurrences of elements taken from S. We define an ordering on all finite multisets over S that is induced by the given ordering on S. This multiset ordering is shown to be well-founded. The value of the multiset ordering is that it permits the use of relatively simple and intuitive termination functions in otherwise difficult termination proofs. In particular, we apply the multiset ordering to prove the termination of production systems, programs defined in terms of sets of rewriting rules. An extended version of this paper appeared as Memo AIM-310, Stanford Artificial Intelligence Laboratory, Stanford, California.

UR - http://www.scopus.com/inward/record.url?scp=85036633503&partnerID=8YFLogxK

U2 - 10.1007/3-540-09510-1_15

DO - 10.1007/3-540-09510-1_15

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AN - SCOPUS:85036633503

SN - 9783540095101

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 188

EP - 202

BT - Automata, Languages and Programming - 6th Colloquium

A2 - Maurer, Hermann A.

PB - Springer Verlag

T2 - 6th International Colloquium on Automata, Languages and Programming, ICALP 1979

Y2 - 16 July 1979 through 20 July 1979

ER -