Related papers: Partial Order Infinitary Term Rewriting
A `whole-part' theory is developed for a set of finite quantum systems $\Sigma (n)$ with variables in ${\mathbb Z}(n)$. The partial order `subsystem' is defined, by embedding various attributes of the system $\Sigma (m)$ (quantum states,…
This paper studies 3-polygraphs as a framework for rewriting on two-dimensional words. A translation of term rewriting systems into 3-polygraphs with explicit resource management is given, and the respective computational properties of each…
The purposes of this note are the following two; we first generalize Okada-Takeuti's well quasi ordinal diagram theory, utilizing the recent result of Dershowitz-Tzameret's version of tree embedding theorem with gap conditions. Second, we…
Partial incorrectness logic (partial reverse Hoare logic) has recently been introduced as a new Hoare-style logic that over-approximates the weakest pre-conditions of a program and a post-condition. It is expected to verify systems where…
We report on an inversion tool for a class of oriented conditional constructor term rewriting systems. Four well-behaved rule inverters ranging from trivial to full, partial and semi-inverters are included. Conditional term rewriting…
We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…
We present a method for the enumeration of restricted words over a finite alphabet. Restrictions are described through the inclusion or exclusion of suitable building blocks used to construct the words by concatenation. Our approach, which…
We introduce a general theory of quantitative and metric rewriting systems, namely systems with a rewriting relation enriched over quantales modelling abstract quantities. We develop theories of abstract and term-based systems, refining…
First-order applicative term rewriting systems provide a natural framework for modeling higher-order aspects. In earlier work we introduced an uncurrying transformation which is termination preserving and reflecting. In this paper we…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
The infinitary lambda calculi pioneered by Kennaway et al. extend the basic lambda calculus by metric completion to infinite terms and reductions. Depending on the chosen metric, the resulting infinitary calculi exhibit different notions of…
Inverse optimization has been increasingly used to estimate unknown parameters in an optimization model based on decision data. We show that such a point estimation is insufficient in a prescriptive setting where the estimated parameters…
We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite…
An adaptive regularization algorithm using high-order models is proposed for partially separable convexly constrained nonlinear optimization problems whose objective function contains non-Lipschitzian $\ell_q$-norm regularization terms for…
For the whole class of linear term rewriting systems, we define \emph{bottom-up rewriting} which is a restriction of the usual notion of rewriting. We show that bottom-up rewriting effectively inverse-preserves recognizability and analyze…
Different notions for order convergence have been considered by various authors. Associated to every notion of order convergence corresponds a topology, defined by taking as the closed sets those subsets of the poset satisfying that no net…
We introduce a novel logical notion--partial entailment--to propositional logic. In contrast with classical entailment, that a formula P partially entails another formula Q with respect to a background formula set \Gamma intuitively means…
We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating…
We construct a monadic second-order sentence that characterizes the ternary relations that are the betweenness relations of finite or infinite partial orders. We prove that no first-order sentence can do that. We characterize the partial…
Conditional term rewriting is an intuitive yet complex extension of term rewriting. In order to benefit from the simpler framework of unconditional rewriting, transformations have been defined to eliminate the conditions of conditional term…