Nonterminal complexity of tree controlled grammars

This paper studies the nonterminal complexity of tree controlled grammars. It is proved that the number of nonterminals in tree controlled grammars without erasing rules leads to an infinite hierarchy of families of tree controlled languages, while every recursively enumerable language can be generated by a tree controlled grammar with erasing rules and at most nine nonterminals.     

Algorithms for the compilation of regular expressions into PLAs

The language of regular expressions is a useful one for specifying certain sequential processes at a very high level. They allow easy modification of designs for circuits, like controllers, that are described by patterns of events they must recognize and the responses they must make to those patterns. This paper discusses the compilation of such expressions into specifications for programmable logic arrays (PLAs) that will implement the required function. A regular expression is converted into a nondeterministic finite automaton, and then the automaton states are encoded as values on wires that are inputs and outputs of a PLA. The translation of regular expressions into nondeterministic automata by two different methods is discussed, along with the advantages of each method. A major part of the compilation problem is selection of good state codes for the nondeterministic automata; one successful strategy and its application to microcode compaction is explained in the paper.Research supported by DARPA Contract N00039-83-C-0136 and NSF Grant MCS-82-03405.     

On the descriptional complexity of scattered context grammars

This paper proves that every recursively enumerable language is generated by a scattered context grammar with no more than four nonterminals and three non-context-free productions. In its conclusion, it gives an overview of the results and open problems concerning scattered context grammars and languages.     

The hardest linear conjunctive language

This paper demonstrates that the P-complete language of yes-instances of Circuit Value Problem under a suitable encoding can be generated by a linear conjunctive grammar, or, equivalently, accepted by a triangular trellis automaton. This result has several implications on the properties of the languages generated by conjunctive grammars of the general form and on the relationship between the abstract models of parallel computation.     

On the complexity of computing the profinite closure of a rational language

Profinite topology is used in the classification of rational languages. In particular, several important decidability problems, related to the Malcev product, reduce to the computation of the closure of a rational language in the profinite topology. It is known that, given a rational language by a deterministic automaton, computing a deterministic automaton accepting its profinite closure can be done with an exponential upper bound. This paper is dedicated the study of a lower bound for this problem: we prove that, in some cases, if the alphabet contains at least three letters, it requires an exponential time.     

Two-way deterministic automata with two reversals are exponentially more succinct than with one reversal

We prove that limiting the number of reversals from two to one can cause an exponential blow-up in the size of two-way deterministic automaton.     

判定非确定离散事件系统稳定性的多项式复杂度算法

本文讨论基于非确定自动机,形式语言模型的非确定离散事件系统稳定性的多项式算法.在引入拟距离的概念之后.根据拟距离形式化地定义了非确定离散事件系统稳定性.以往判定非确定离散事件系统稳定性的算法基于系统的观测器实现,该观测器在结构上具有指数复杂度,因此本文分析系统结构和观测器结构之间的关系,基于对系统状态对的讨论,提出了判定系统稳定性的有效多项式搜索算法.     

Traced communication complexity of cellular automata

We study cellular automata with respect to a new communication complexity problem: each of two players know half of some finite word, and must be able to tell whether the state of the central cell will follow a given evolution, by communicating as little as possible between each other. We present some links with classical dynamical concepts, especially equicontinuity, expansivity, entropy and give the asymptotic communication complexity of most elementary cellular automata.