Rewriting is essential for efficient bit-vector SMT solving. The rewriting algorithm commonly used by modern SMT solvers iteratively applies a set of ad hoc rewriting rules hard-coded into the solver to simplify the given formula at the preprocessing stage. This paper proposes an automatic approach to rewriting. The solver starts each invocation with an empty set of rewriting rules. The set is ...

For alternate Cantor real base numeration systems we generalize the result of Frougny and Solomyak on arithmetics set numbers with finite expansion. We provide a class bases which satisfy so-called finiteness property. The proof uses rewriting rules language expansions in corresponding system. is constructive provides method for performing addition bases.

In the rule-based equivalent transformation (RBET) paradigm, where computation is based on meaning-preserving transformation of declarative descriptions, a set of rewriting rules is regarded as a program. The syntax for a large class of rewriting rules is determined. The incorporation of meta-variables of two different kinds enables precise control of rewriting-rule instantiations. As a result,...

Domain independent planners can produce better-quality plans through the use of domain-speci c knowledge, typically encoded as search control rules. The planning-by-rewriting approach has been proposed as an alternative technique for improving plan quality. We present a system that automatically learns plan rewriting rules and compare it with a system that automatically learns search control ru...

We present a translation function from nominal rewriting systems (NRSs) to combinatory reduction systems (CRSs), transforming closed nominal rules and ground nominal terms to CRSs rules and terms, respectively, while preserving the rewriting relation. We also provide a reduction-preserving translation in the other direction, from CRSs to NRSs, improving over a previously defined translation. Th...

In this paper we introduce Associative Commutative Distributive Term Rewriting (ACDTR), a rewriting language for rewriting logical formulae. ACDTR extends AC term rewriting by adding distribution of conjunction over other operators. Conjunction is vital for expressive term rewriting systems since it allows us to require that multiple conditions hold for a term rewriting rule to be used. ACDTR u...

We address the issue of Ontology-Based Data Access which consists of exploiting the semantics expressed in ontologies while querying data. Ontologies are represented in the framework of existential rules, also known as Datalog+/-. We focus on the backward chaining paradigm, which involves rewriting the query (assumed to be a conjunctive query, CQ) into a set of CQs (seen as a union of CQs). The...

Today it is wildly recognized that optimization based on rewriting leads to faster query execution. The role of a query rewriting grows significantly when a query defined in terms of some view is processed. Using views is a good idea for building flexible virtual data integration systems with declarative query support. At present time such systems tend to be based on the XML data model and use ...

Gene assembly is an intricate biological process that has been studied formally and modeled through string and graph rewriting systems. Recently, a restriction of the general (intramolecular) model, called simple gene assembly, has been introduced. This restriction has subsequently been defined as a string rewriting system. We show that by extending the notion of overlap graph it is possible to...

We introduce rewriting with two sets of rules, the rst interpreted equa-tionally and the second not. A semantic view considers equational rules as deening an equational theory and reduction rules as deening a rewrite relation modulo this theory. An operational view considers both sets of rules as similar. We introduce suucient properties for these two views to be equivalent (up to diierent noti...