On Varieties of Literally Idempotent Languages
نویسندگان
چکیده
A language L ⊆ A∗ is literally idempotent in case that uav ∈ L if and only if uav ∈ L for each u, v ∈ A∗, a ∈ A. Such classes result naturally by taking all literally idempotent languages in a classical (positive) variety or by considering a certain closure operator. We initiate their systematic study. Various classes of such languages can be characterized using syntactic methods. A starting example is the class of all finite unions of B∗ 1B ∗ 2 . . . B ∗ k where B1, . . . , Bk are subsets of a given alphabet A. MSC 2000 Classification: 68Q45 Formal languages and automata
منابع مشابه
Literally idempotent languages and their varieties - two letter case
A language L ⊆ A∗ is literally idempotent in case that uav ∈ L if and only if uav ∈ L, for each u, v ∈ A∗, a ∈ A. We already studied classes of such languages closely related to the (positive) varieties of the famous StraubingThérien hierarchy. In the present paper we start a systematic study of literal varieties of literally idempotent languages, namely we deal with the case of two letter alph...
متن کاملSmall Conjunctive Varieties of Regular Languages
The author’s modification of Eilenberg theorem relates the so-called conjunctive varieties of regular languages with pseudovarieties of idempotent semirings. Recent results by Pastijn and his co-authors lead to the description of the lattice of all (pseudo)varieties of idempotent semirings with idempotent multiplication. We describe here the corresponding 78 varieties of languages.
متن کامل(Extended Version) Algebraic Characterization of the Class of Languages recognized by Measure Only Quantum Automata
We study a model of one-way quantum automaton where only measurement operations are allowed (MOn-1qfa). We give an algebraic characterization of LMO(Σ), showing that the syntactic monoids of the languages in LMO(Σ) are exactly the J-trivial literally idempotent syntactic monoids, where J is the Green’s relation determined by two-sided ideals. We also prove that LMO(Σ) coincides with the literal...
متن کاملAlgebraic Characterization of the Class of Languages Recognized by Measure Only Quantum Automata
We study a model of one-way quantum automaton where only measurement operations are allowed (MOn-1qfa). We give an algebraic characterization of LMO(Σ), showing that the syntactic monoids of the languages in LMO(Σ) are exactly the literal pseudovariety of J-trivial literally idempotent monoids, where J is the Green’s relation determined by two-sided ideals. We also prove that LMO(Σ) coincides w...
متن کاملProduct preservation and stable units for reflections into idempotent subvarieties
We give a necessary and sufficient condition for the preservation of finite products by a reflection of a variety of universal algebras into an idempotent subvariety. It is also shown that simple and semi-left-exact reflections into subvarieties of universal algebras are the same. It then follows that a reflection of a variety of universal algebras into an idempotent subvariety has stable units...
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 42 شماره
صفحات -
تاریخ انتشار 2008