This paper gives decidable conditions for when a nitely generated subgroup of a free group is the fundamental group of a Sch utzenberger automaton corresponding to a monoid presentation of an inverse monoid. Also, generalizations are given to speciic types of inverse monoids as well as to monoids which are \nearly inverse." This result has applications to computing membership for inverse monoid...

It has been shown [6] that, within the McAlister inverse monoid [9], whose elements can be seen as overlapping one-dimensional tiles, the class of languages recognizable by finite monoids collapses compared with the class of languages definable in Monadic Second Order Logic (MSO). This paper aims at capturing the expressive power of the MSO definability of languages of tiles by means of a weake...

An atomic monoid M is called a length-factorial (or an other-half-factorial monoid) if for each non-invertible element x ? no two distinct factorizations of have the same length. The notion length-factoriality was introduced by Coykendall and Smith in 2011 as dual well-studied half-factoriality. They proved that setting integral domains, can be taken alternative definition unique factorization ...

We give a monoid presentation in terms of generators and defining relations for the partial analogue of the finite dual inverse symmetric monoid. AMS 2000 Mathematical Subject Classification 20M05, 68R15, 20M20.

In 1987 Squier defined the notion of finite derivation type for a finitely presented monoid. To do this, he associated a 2-complex to the presentation. The monoid then has finite derivation type if, modulo the action of the free monoid ring, the 1-dimensional homotopy of this complex is finitely generated. Cremanns and Otto showed that finite derivation type implies the homological finiteness c...

The syntactic monoid of a language is generalized to the level of a symmetric monoidal closed category D. This allows for a uniform treatment of several notions of syntactic algebras known in the literature, including the syntactic monoids of Rabin and Scott (D “ sets), the syntactic semirings of Polák (D “ semilattices), and the syntactic associative algebras of Reutenauer (D = vector spaces)....

Generalizing results of Otto & Ruškuc, this paper shows that every finitely generated submonoid of a monoid presented by a confluent finite special rewriting system admits an automatic structure that is simultaneously rr-, `r-, r`-, and ``-automatic; and that every finitely generated submonoid of a monoid presented by a confluent regular monadic rewriting system admits an automatic structure th...

Pierre McKenzie and Sambuddha Roy pointed out that the proof of statements (b) and (c) in Theorem 7.3 are buggy. The main flaw is that the identity e of the group F may not be the identity of the monoid, and so the claim that w ∈ (A F,r) * ⇐⇒ w ∈ Test does not work. In this corrigendum, we show: • With a slight change to Definition 7.1, the statement of Theorem 7.3 holds unchanged. In our opini...

In this paper, a Gröbner-Shirshov basis for the Chinese monoid is obtained and an algorithm for the normal form of the Chinese monoid is given. AMS Mathematics Subject Classification (2000): 16S15, 16S35, 20M25.

We deene a standard of eeectiveness for a database calculus relative to a query language. EEectiveness judges suitability to serve as a processing framework for the query language, and comprises aspects of coverage, manipulability and eecient evaluation. We present the monoid calculus, and argue its eeectiveness for object-oriented query languages, exempliied by OQL of ODMG-93. The monoid calcu...