Finite idempotent groupoids and regular languages

Finite idempotent groupoids and 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...

Regular Languages and Finite Automata

Regular Languages and Finite Automata

In 1943, McCulloch and Pitts [4] published a pioneering work on a model for studying the behavior of the nervous systems. Following up on the ideas of McCulloch and Pitts, Kleene [3] wrote the first paper on finite automata and regular expressions. A finite automaton can be considered as the simplest machine model in that the machine has a finite memory; that is, the memory size is independent ...

Non-idempotent left symmetric left distributive groupoids

Subdirectly irreducible non-idempotent groupoids satisfying x · xy = y and x · yz = xy · xz are studied.