Strongly locally testable semigroups with commuting idempotents and related languages
نویسنده
چکیده
If we consider words over the alphabet which is the set of all elements of a semigroup S, then such a word determines an element of S: the product of the letters of the word. S is strongly locally testable if whenever two words over the alphabet S have the same factors of a fixed length k, then the products of the letters of these words are equal. We had previously proved [19] that the syntactic semigroup of a rational language L is strongly locally testable if and only if L is both locally and piecewise testable. We characterize in this paper the variety of strongly locally testable semigroups with commuting idempotents and, using the theory of implicit operations on a variety of semigroups, we derive an elementary combinatorial description of the related variety of languages.
منابع مشابه
Right and left strongly locally testable semigroups and languages
The objective of this paper is to de ne and characterize the families of right (left) strongly locally testable languages (RSLT and LSLT ) and semigroups (RSLTS and LSLTS). Given k > 0, the membership of a w ord x to a RSLT (RSTk) language can be decided by exploring the segments of length k of x, as well as considering the order of appearance of those segments when we scan the pre xes of x. A ...
متن کاملOn the Varieties of Languages Associated with Some Varieties of Finite Monoids with Commuting Idempotents
Eilenberg has shown that there is a one-to-one correspondence between varieties of finite monoids and varieties of recognizable languages. In this paper, we give a description of a variety of languages close to the class of piecewise testable languages considered by I. Simon. The corresponding variety of monoids is the variety of J -trivial monoids with commuting idempotents. This result is the...
متن کاملFinite Aperiodic Semigroups with Commuting Idempotents and Generalizations
Among the most important and intensively studied classes of semigroups are finite semigroups, regular semigroups and inverse semigroups. Finite semigroups arise as syntactic semigroups of regular languages and as transition semigroups of finite automata. This connection has lead to a large and deep literature on classifying regular languages by means of algebraic properties of their correspondi...
متن کاملPower centralized semigroups
A semigroup is said to be power centralized if for any pair of elements there exists a power of the first one commuting with the second one. We describe the structure of power centralized groups and semigroups. In particular, we present several characterizations of periodic semigroups with central idempotents.
متن کاملAn application of a Theorem of Ash to finite covers
Weakly left ample semigroups form a class of semigroups that are (2; 1)-subalgebras of semigroups of partial transformations, where the unary operation takes a transformation to the identity map in the domain of. They are semigroups with commuting idempotents such that the e R-class of any element a contains a (necessarily unique) idempotent a + , e R is a left congruence, and the ample identit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- ITA
دوره 33 شماره
صفحات -
تاریخ انتشار 1999