M. Okada and A. Steel, Ordering structures and the Knuth-Bendix completion algorithm, in: Proceedings of the Allerton Conference on Communication, Control and Computing, Monticello, IL, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....by order type ff, the Well Orderings of Algebra and Kruskal s Theorem 31 associated multiset path ordering is order isomorphic to (ff; 0) in FefermanSch utte notation [8] The order types of lexicographic path orderings were seldom mentioned in the literature. Some partial results are found in [28, 10]. From the previous theorem, we know that the order types of the lexicographic path orderings are much greater than the corresponding multiset path orderings. Recall that Ackermann orderings are linearizations of algebra embeddings. So we have a lower bound for the order type of Bad (A) Consider ....

M. Okada and A. Steel, Ordering structures and the Knuth-Bendix completion algorithm, in: Proceedings of the Allerton Conference on Communication, Control and Computing, Monticello, IL, 1988.

.... of the natural numbers [ Dijkstra, 1976; Gries, 1981 ] but lexicographic orderings ( n ) also play an important part [ Manna, 1974 ] Occasionally, larger orderings have been used (for example, Dershowitz and Manna, 1979; Dershowitz, 1987 ] see [ Dershowitz, 1987; Dershowitz and Okada, 1988; Cichon, 1990 ] The riddle above is a termination question on binary trees, one of the most pervasive data structures used in computer science. Like numbers, binary trees can be well ordered in many ways. In this paper, we give natural principles that such orderings ought to satisfy. We ....

....than or equivalent to its subtrees; that is, cons(x; y) x; y; for all trees x; y. Principle 2 (Monotonicity) Replacing a subtree by a greater or equivalent one results in a greater or equivalent tree; that is, x y ) cons(x; z) cons(y; z) cons(z; x) cons(z; y) for all trees x; y; z. Okada and Steele [ 1988 ] relate any ordering on finite trees satisfying such principles to Ackermann s ordinal notation. By deleting in a tree, we mean replacing a subtree by one of its subtrees; inserting is the inverse operation. Lemma 1. Deleting (inserting) results in a smaller (greater) or equivalent tree. ....

M. Okada and A. Steele. Ordering structures and the Knuth-Bendix completion algorithm. In Proceedings of the Allerton Conference on Communication, Control, and Computing, Monticello, IL, 1988.

.... Delta Delta Delta Gamma Gamma Delta Delta Delta : BEFORE AFTER Figure 1: Hercules versus Hydra. All the orderings described in this section are simplification orderings [ Dershowitz, 1982 ] a tree is greater than any homeomorphically embedded tree. It has been shown [ Okada and Steele, 1988 ] that all such orderings on finite trees are initial segments of Ackermann s notation (what we got with supertrees) which itself can be proved well ordered by appealing to Kruskal s Tree Theorem. The well orderings of rational and infinite trees are consequences of generalizations of the Tree ....

....n 1 y; r n hB; y; zii r n hx; y; zi z hx; y; zi hx; y; zi A nodes are lexicographic; B nodes are sums, summands of which r duplicates for p to reduce; G stands for Gremlin ; the bar keeps track of what p has done. Even bigger battles and their associated ordinals are described in [ Okada, 1988 ] 4 Conclusion We conclude with the function f of Figure 2 (a repaired riddle from [ Dershowitz and Reingold, 1992 ] Show that the sequence t f(t) f(f(t) Delta Delta Delta f n (t) Delta Delta Delta always ends in a leaf starting with any finite binary tree t with foliage of two ....

Mitsuhiro Okada and Adam Steele. Ordering structures and the Knuth-Bendix completion algorithm. In Proceedings of the Allerton Conference on Communication, Control, and Computing, Monticello, IL, 1988.

No context found.

Okada, M. and A. Steele, Ordering structures and the Knuth-Bendix completion algorithm, Unpublished manuscript, Dept. Computer Science, Concordia Univ., Montreal, Canada.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC