Conservative groupoids recognize only regular languages

Conservative Groupoids Recognize Only Regular Languages

The notion of recognition of a language by a finite semigroup can be generalized to recognition by finite groupoids, i.e. sets equipped with a binary operation ‘ · ’ which is not necessarily associative. It is well known that L can be recognized by a groupoid iff L is context-free. But it is also known that some subclasses of groupoids can only recognize regular languages. For example, loops re...

Finite idempotent groupoids and regular languages

Two-way non-deterministic finite automata with a write-once track recognize regular languages only

The basic finite automata model has been extended over the years with different acceptance modes (non-determinism, alternation), new or improved devices (two-way heads, pebbles, nested pebbles) or with cooperation. None of these additions permits recognition of non-regular languages. The purpose of this work is to investigate a new extension which is inspired by an extension of 2DPDAs. Mogensen...

Finite Loops Recognize Exactly the Regular Open Languages

In this paper, we characterize exactly the class of languages that are recognizable by nite loops, i.e. by cancellative binary algebras with an identity. This turns out to be the well-studied class of regular open languages. Our proof technique is interesting in itself: we generalize the operation of block product of monoids, which is so useful in the associative case, to the situation where th...

Linearization of Regular Proper Groupoids

Let G be a Lie groupoid over M such that the target-source map from G to M ×M is proper. We show that, if O is an orbit of finite type (i.e. which admits a proper function with finitely many critical points), then the restriction G|U of G to some neighborhood U of O in M is isomorphic to a similar restriction of the action groupoid for the linear action of the transitive groupoid G|O on the nor...