Detecting patterns in finite regular and context-free languages

We consider some natural variations on the following classic pattern-matching problem: given an NFA M over the alphabet Σ and a pattern p over some alphabet Δ, does there exist a word x∈L(M) such that x matches p? We consider the restricted problem where M only accepts a finite language. We also consider the variation where only some factor of x is required to match the pattern p. We show that both of these problems are NP-complete. We also consider the same problems for context-free grammars; in this case the problems become PSPACE-complete.     

Closure properties of linear context-free tree languages with an application to optimality theory

Context-free tree grammars, originally introduced by Rounds [Math. Systems Theory 4(3) (1970) 257–287], are powerful grammar devices for the definition of tree languages. The properties of the class of context-free tree languages have been studied for more than three decades now. Particularly important here is the work by Engelfriet and Schmidt [J. Comput. System Sci. 15(3) (1977) 328–353, 16(1) (1978) 67–99]. In the present paper, we consider a subclass of the class of context-free tree languages, namely the class of linear context-free tree languages. A context-free tree grammar is linear, if no rule permits the copying of subtrees. For this class of linear context-free tree languages we show that the grammar derivation mode, which is very important for the general class of context-free tree languages, is immaterial. The main result we present is the closure of the class of linear context-free tree languages under linear frontier-to-root tree transduction mappings. Two further results are the closure of this class under linear root-to-frontier tree transduction mappings and under intersection with regular tree languages.     

上下文无关语言句子的反向自然枚举

在测试基于复杂数据结构的程序时,需要用到上下文无关语言句子的枚举.基于上下文无关语言按推导树高度的分层构造,提出了句子的反向自然枚举算法.通过堆、层、簇和长方体将句子划分为有穷集合序列,该算法的时间效率为O(n),n是被枚举句子的长度.实验数据表明,该算法是高效的,且应用更加便利.     

Pattern Matching Compilation of Functions Defined in Context—Free Languages

LFC is a functional language based on recursive functions defined in context-free languages.In this paper,a new pattern matching algorithm for LFC is presented,which can represent a sequence of patterns as an integer by an encoding method.It is a rather simple method and produces efficient case-expressions for pattern matching definitions of LFC.The algorithm can also be used for other functional languages,but for nested patterns it may become complicated and further studies are needed.     

量子上下文无关文法的代数性质

提出了量子上下文无关文法（l-VCFG）的概念,并研究了其具有的代数性质;证明了量子上下文无关文法（l-VCFG）和Chomsky范式文法（l-VCNF）以及Greibach范式文法（l-VGNF）的相互等价性;详细研究了量子上下文无关语言的代数刻画以及对于正则运算的封闭性。     

Lukasiewicz逻辑值上下文无关语言的代数刻画

提出了基于Lukasiewicz逻辑的下推自动机（l-VPDA）的概念,从代数角度研究了此类自动机的性质,同时建立此类自动机的代数刻画,即利用模糊状态构造,证明了任意以终状态方式接受模糊语言的l-VPDA与状态转移为经典函数且具有l值模糊终状态的l-VPDA间的相互等价性;并证明任意以空栈方式接受模糊语言的l-VPDA与状态转移除一步转移为模糊的以外,其余都是经典函数的l-VPDA是相互等价的;详细研究了l-值模糊上下文无关语言的代数和层次刻画,以及对于正则运算的封闭性。     

The language intersection problem for non-recursive context-free grammars

We prove that, given as input two context-free grammars, deciding non-emptiness of intersection of the two generated languages is PSPACE-complete if at least one grammar is non-recursive. The problem remains PSPACE-complete when both grammars are non-recursive and deterministic. Also investigated are generalizations of the problem to several context-free grammars, of which a certain number are non-recursive.     

量化上下文无关语言的代数性质

通过引入量化下推自动机与量化上下文无关文法的定义,研究了以两种不同方式接受语言的量化下推自动机等价性问题,证明了在可交换的双幺赋值幺半群上,量化下推自动机接受的语言与量化上下文无关文法生成的语言相同。     

The Turing degree of the inherent ambiguity problem for context-free languages

The inherent ambiguity question for context-free languages is shown to be in the Turing degree of unsolvability O”. The method used is to show that the inherent ambiguity question is equivalent to the finiteness question for r.e. sets which is in degree O”. The proof associates a context-free language with each Turing machine. The language has a natural closed-form definition in terms of the Turing machine. The associated language is inherently ambiguous precisely iof the Turing machine accepts an infinite set.     

More decidable instances of Post's correspondence problem: beyond counting

We present a new technique to decide or reduce instances of Post's correspondence problem. It generalizes balance arguments to a consideration about some special context-free languages which allow the combination with other decision (or reduction) techniques. In spite of its simplicity, the new technique is able to decide more instances than known techniques.