Craig Squier proved that, if a monoid can be presented by a finite convergent string rewriting system, then it satisfies the homological finiteness condition left-FP3. Using this result, he constructed finitely presentable monoids with a decidable word problem, but that cannot be presented by finite convergent rewriting systems. Later, he introduced the condition of finite derivation type, whic...

Narrowing is a procedure that was first studied in the context of equational E-unification and that has been used in a wide range of applications. The classic completeness result due to Hullot states that any term rewriting derivation starting from an instance of an expression can be ‘lifted’ to a narrowing derivation, whenever the substitution employed is normalized. In this paper we adapt the...

The basic algebraic structures within the categories of derivations determined by rewriting systems are presented. The similarity congruence relation in categories of derivations is given in three versions. The syntax category is formed by taking derivations modulo similarity. This category is a free strict monoidal category, a simple form of a 2-category. The syntax category is central to the ...

This paper presents a novel technique called "universal guides" which explores inherent properties of logic grammars (changing variable binding status) in order to characterize tbrmal criteria for termination in a derivation process. The notion of universal guides also offers a new framework in which both parsing and generation can be viewed merely as two different instances of the same generic...

As critical computer systems continue to grow in complexity, the task of showing that they execute correctly becomes more difficult. For this reason, research in software engineering has turned to formal methods, i.e., rigorous approaches to demonstrating the correctness of software systems. Unfortunately, the formal methods currently used in the design of concurrent systems do not provide any ...

Let I be a non-zero left ideal of r-ring M satisfying the condition alpha b beta c= c for all a,b,c, e and alpha, r. We show that contains non-trivial central if is semiprime which admits an appropriate derivations on I, also commutative prime admitting centralizing derivation I. next give some characterizations when generalized act as homomorphisms anti-homomorphisms or two-sided ideals gamma ...

We characterize derivations and 2-local derivations from Mn(A) into Mn(M), n ≥ 2, where A is a unital algebra over C and M is a unital A-bimodule. We show that every derivation D : Mn(A) → Mn(M), n ≥ 2, is the sum of an inner derivation and a derivation induced by a derivation from A to M. We say that A commutes with M if am = ma for every a ∈ A and m ∈ M. If A commutes with M we prove that eve...

We study the subgroup of k -automorphisms of k ⁢ [ x , y ] which commute with a simple derivation d of k ⁢ [ x , y ] . We prove, for instance, that this subgroup is trivial when d is a shamsuddin simple derivation. in the general case of simple derivations, we obtain properties for the elements of this subgroup.