theoretical computer science, an abstract rewriting system (also (abstract) reduction system or abstract rewrite system; abbreviated ARS) is a formalism...

in the most abstract setting of an abstract rewriting system. The usual rules of elementary arithmetic form an abstract rewriting system. For example...

In abstract rewriting, an object is in normal form if it cannot be rewritten any further, i.e. it is irreducible. Depending on the rewriting system, an...

logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems (also...

and mathematical logic a string rewriting system (SRS), historically called a semi-Thue system, is a rewriting system over strings from a (usually finite)...

object, an unlabeled transition system is identical with an (unindexed) abstract rewriting system. If we consider the rewriting relation as an indexed set...

specifically in term rewriting, Newman's lemma, also commonly called the diamond lemma, is a criterion to prove that an abstract rewriting system is confluent...

can be validly manipulated. These are the "rewriting rules"—an integral part of an abstract rewriting system. A common question is whether it is possible...

approach to graph rewriting is term graph rewriting, which involves the processing or transformation of term graphs (also known as abstract semantic graphs)...

The Abstract Rewriting Machine (ARM) is a virtual machine which implements term rewriting for minimal term rewriting systems. Minimal term rewriting systems...

Normalizing (abstract rewriting), an abstract rewriting system in which every object has at least one normal form Normalization property (abstract rewriting), a...

objects in these formal systems. Abstract rewriting systems can operate on these objects. Axiomatic systems, and logic systems build upon axioms, and upon...

Note that the rewriting here is one-way. The word problem is the accessibility problem for symmetric rewrite relations, i.e. Thue systems. The accessibility...

Society Assemblea Regionale Siciliana, Sicilian Regional Assembly Abstract rewriting system in mathematical logic Acoustic resonance spectroscopy Acute radiation...

satisfy the descending chain condition. Noetherian rewriting system, an abstract rewriting system that has no infinite chains. Noetherian scheme, a scheme...

means for a computation to converge or diverge. In abstract rewriting, an abstract rewriting system is called convergent if it is both confluent and terminating...

pathways (P53), ecosystems, and enzyme systems by using his method, abstract rewriting system on multisets (ARMS). In the 1994 science-fiction novel Permutation...

both b and c can be reduced. Viewing the lambda calculus as an abstract rewriting system, the Church–Rosser theorem states that the reduction rules of...

which states that if an (abstract) rewriting system is strongly normalizing and weakly confluent, then the rewriting system is confluent. So, if we can...

Decision tree model External memory model Functional models include: Abstract rewriting systems Combinatory logic General recursive functions Lambda calculus...

studied in the field of graph rewriting. The nomenclature term graph is associated with the field of term graph rewriting, which involves the transformation...

Iron Curtain: a history of the algebraic theory of semigroups" Abstract rewriting system Additive relation, a many-valued homomorphism between modules...

simplified by rewriting before a narrowing step is applied and equations are rejected if the two sides have different constructors at the top. Rewriting and rejection...

get to it (they are confluent). More formally, a preordered set of term rewriting transformations are said to be convergent if they are confluent and terminating...

functions are both linear and regular is called a Linear Context-free Rewriting System (LCFRS). LCFRS is a proper subclass of the GCFGs, i.e. it has strictly...

The Maude system is an implementation of rewriting logic. It is similar in its general approach to Joseph Goguen's OBJ3 implementation of equational logic...

g., contextual analysis. Abstract syntax trees are also used in program analysis and program transformation systems. Abstract syntax trees are data structures...

preorders are preorders (hence the name). Reduction relations in abstract rewriting systems. The encompassment preorder on the set of terms, defined by s...

science – Study of abstract structures described by formal systems Logic translation – Translation of a text into a logical system Rewriting system – Replacing...

In rewriting, a reduction strategy or rewriting strategy is a relation specifying a rewrite for each object or term, compatible with a given reduction...