Some Forbidden Patterns in Automata for Dot-Depth One Languages
نویسنده
چکیده
We deal with the class B of dot-depth one languages which forms level one of the socalled dot-depth hierarchy. For some fixed alphabet A with jAj , a language L A is in the class B if and only if it can be expressed as a Boolean combination of languages u A u A u A A un A un, where ui A and n . This class is the highest level of the dot-depth hierarchy known to be decidable up to now and a number of different characterizations are known. We add here one more in terms of certain patterns that must not appear in the transition graph of deterministic finite automata accepting dot-depth one languages. More precisely, the following levelwise characterization of languages having dot-depth one is known (k ): A language L A is in the class B k if and only if any infinite sequence of words, where each word is a so-called k-extension of its predecessor, has a finite number of alternations with respect to L. It holds that B k B k and B S k B k. We use this characterization to prove a uniform and levelwise “forbidden-pattern” characterization of dot-depth one languages having level k of the type: L B k if and only if none of certain patterns Pk, P k and P k (cf. Figures 4, 5, 6) appears in the transition graph of a deterministic finite automaton accepting L. These patterns are different from other known characterizations of this type for these classes.
منابع مشابه
Concatenation Hierarchies and Forbidden Patterns
We make the following progress on the dot–depth problem: (1) We introduce classes CB n and CL n of starfree languages defined via forbidden patterns in finite automata. It is shown for all n 0 that CB n (CL n) contains level n + 1=2 of the dot–depth hierarchy (Straubing–Thérien hierarchy, resp.). Since we prove that CB n and CL n have decidable membership problems, this yields a lower bound alg...
متن کاملGeneralized Deterministic Languages and their Automata: A Characterization of Restricted Temporal Logic
Let TL X F TL F be the class of formulas of temporal logic, where as the only temporal operatorsX (next) andF (eventually) are allowed (onlyF is allowed, resp.). For a class TL X F let L be the class of -definable languages. Among others, characterizations of L TL X F and L TL F in terms of forbidden patterns in finite automata are known. Here we ask for every bound k on the number of nested us...
متن کاملCounting with Counterfree Automata
We study the power of balanced regular leaf-languages. First, we investigate (i) regular languages that are polylog-time reducible to languages in dot-depth 1/2 and (ii) regular languages that are polylog-time decidable. For both classes we provide • forbidden-pattern characterizations, and • characterizations in terms of regular expressions. Both classes are decidable. The intersection of clas...
متن کاملNovel Defect Terminolgy Beside Evaluation And Design Fault Tolerant Logic Gates In Quantum-Dot Cellular Automata
Quantum dot Cellular Automata (QCA) is one of the important nano-level technologies for implementation of both combinational and sequential systems. QCA have the potential to achieve low power dissipation and operate high speed at THZ frequencies. However large probability of occurrence fabrication defects in QCA, is a fundamental challenge to use this emerging technology. Because of these vari...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999