71 research outputs found
Soundness of Unravelings for Deterministic Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity
Unravelings are transformations from a conditional term rewriting
system (CTRS, for short) over an original signature into an
unconditional term rewriting systems (TRS, for short) over an extended
signature. They are not sound for every CTRS w.r.t. reduction, while
they are complete w.r.t. reduction. Here, soundness w.r.t. reduction
means that every reduction sequence of the corresponding unraveled
TRS, of which the initial and end terms are over the original
signature, can be simulated by the reduction of the original CTRS. In
this paper, we show that an optimized variant of Ohlebusch\u27s
unraveling for deterministic CTRSs is sound w.r.t. reduction if the
corresponding unraveled TRSs are left-linear or both right-linear and
non-erasing. We also show that soundness of the variant implies that
of Ohlebusch\u27s unraveling
Soundness of Unravelings for Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity
Unravelings are transformations from a conditional term rewriting system
(CTRS, for short) over an original signature into an unconditional term
rewriting systems (TRS, for short) over an extended signature. They are not
sound w.r.t. reduction for every CTRS, while they are complete w.r.t.
reduction. Here, soundness w.r.t. reduction means that every reduction sequence
of the corresponding unraveled TRS, of which the initial and end terms are over
the original signature, can be simulated by the reduction of the original CTRS.
In this paper, we show that an optimized variant of Ohlebusch's unraveling for
a deterministic CTRS is sound w.r.t. reduction if the corresponding unraveled
TRS is left-linear or both right-linear and non-erasing. We also show that
soundness of the variant implies that of Ohlebusch's unraveling. Finally, we
show that soundness of Ohlebusch's unraveling is the weakest in soundness of
the other unravelings and a transformation, proposed by Serbanuta and Rosu, for
(normal) deterministic CTRSs, i.e., soundness of them respectively implies that
of Ohlebusch's unraveling.Comment: 49 pages, 1 table, publication in Special Issue: Selected papers of
the "22nd International Conference on Rewriting Techniques and Applications
(RTA'11)
Unifying the Knuth-Bendix, recursive path and polynomial orders
We introduce a simplification order called the weighted path order (WPO). WPO compares weights of terms as in the Knuth-Bendix order (KBO), while WPO allows weights to be computed by an arbitrary interpretation which is weakly monotone and weakly simple. We investigate summations, polynomials and maximums for such interpretations. We show that KBO is a restricted case of WPO induced by summations, the polynomial order (POLO) is subsumed by WPO induced by polynomials, and the lexicographic path order (LPO) is a restricted case of WPO induced by maximums. By combining these interpretations, we obtain an instance of WPO that unifies KBO, LPO and POLO. We also present SMT encodings of our orders, as well as incorporating them in the dependency pair framework
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