اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدParikhs Theorem: A simple and direct automaton construction
106
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Parikhs theorem states that the Parikh image of a context-free language is semilinear or, equivalently, that every context-free language has the same Parikh image as some regular language. We present a very simple construction that, given a context-free grammar, produces a finite automaton recognizing such a regular language.
قيم البحث
اقرأ أيضاً
The commutative ambiguity of a context-free grammar G assigns to each Parikh vector v the number of distinct leftmost derivations yielding a word with Parikh vector v. Based on the results on the generalization of Newtons method to omega-continuous s
emirings, we show how to approximate the commutative ambiguity by means of rational formal power series, and give a lower bound on the convergence speed of these approximations. From the latter result we deduce that the commutative ambiguity itself is rational modulo the generalized idempotence identity k=k+1 (for k some positive integer), and, subsequently, that it can be represented as a weighted sum of linear sets. This extends Parikhs well-known result that the commutative image of context-free languages is semilinear (k=1). Based on the well-known relationship between context-free grammars and algebraic systems over semirings, our results extend the work by Green et al. on the computation of the provenance of Datalog queries over commutative omega-continuous semirings.
We provide a direct proof of Agafonovs theorem which states that finite state selection preserves normality. We also extends this result to the more general setting of shifts of finite type by defining selections which are compatible the shift. A sli
ghtly more general statement is obtained as we show that any Markov measure is preserved by finite state compatible selection.
This paper addresses a decision problem highlighted by Grigorchuk, Nekrashevich, and Sushchanskii, namely the finiteness problem for automaton (semi)groups. For semigroups, we give an effective sufficient but not necessary condition for finiteness
and, for groups, an effective necessary but not sufficient condition. The efficiency of the new criteria is demonstrated by testing all Mealy automata with small stateset and alphabet. Finally, for groups, we provide a necessary and sufficient condition that does not directly lead to a decision procedure.
The finiteness problem for automaton groups and semigroups has been widely studied, several partial positive results are known. However we prove that, in the most general case, the problem is undecidable. We study the case of automaton semigroups. Gi
ven a NW-deterministic Wang tile set, we construct an Mealy automaton, such that the plane admit a valid Wang tiling if and only if the Mealy automaton generates a finite semigroup. The construction is similar to a construction by Kari for proving that the nilpotency problem for cellular automata is unsolvable. Moreover Kari proves that the tiling of the plane is undecidable for NW-deterministic Wang tile set. It follows that the finiteness problem for automaton semigroup is undecidable.
Viral kinetics have been extensively studied in the past through the use of spatially homogeneous ordinary differential equations describing the time evolution of the diseased state. However, spatial characteristics such as localized populations of d
ead cells might adversely affect the spread of infection, similar to the manner in which a counter-fire can stop a forest fire from spreading. In order to investigate the influence of spatial heterogeneities on viral spread, a simple 2-D cellular automaton (CA) model of a viral infection has been developed. In this initial phase of the investigation, the CA model is validated against clinical immunological data for uncomplicated influenza A infections. Our results will be shown and discussed.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
