相关论文: An Extension of Parikh's Theorem beyond Idempotenc…

We consider commutative regular and context-free grammars, or, in other words, Parikh images of regular and context-free languages. By using linear algebra and a branching analog of the classic Euler theorem, we show that, under an…

We investigate commutative images of languages recognised by register automata and grammars. Semi-linear and rational sets can be naturally extended to this setting by allowing for orbit-finite unions instead of only finite ones. We prove…

Parikh's Theorem says that the Parikh image of a context-free language is semilinear. We give a short proof of Parikh's Theorem using the formulation of Verma, Seidl, and Schwentick in terms of Presburger arithmetic. The proof relies on an…

We consider Parikh images of languages accepted by non-deterministic finite automata and context-free grammars; in other words, we treat the languages in a commutative way --- we do not care about the order of letters in the accepted word,…

Parikh's 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…

We show a new and constructive proof of the following language-theoretic result: for every context-free language L, there is a bounded context-free language L' included in L which has the same Parikh (commutative) image as L. Bounded…

Parikh's Theorem states that every context-free grammar (CFG) is equivalent to some regular CFG when the ordering of symbols in the words is ignored. The same is not true for the so-called weighted CFGs, which additionally assign a weight…

We show that the Parikh image of the language of an NFA with n states over an alphabet of size k can be described as a finite union of linear sets with at most k generators and total size 2^{O(k^2 log n)}, i.e., polynomial for all fixed k…

It has been conjectured that the Parikh (commutative) image of every language over an infinite alphabet recognized by an automaton with registers is defined by a rational expression. This conjecture is known to hold for all languages…

We investigate the conversion of one-way nondeterministic finite automata and context-free grammars into Parikh equivalent one-way and two-way deterministic finite automata, from a descriptional complexity point of view. We prove that for…

In weighted automata theory, many classical results on formal languages have been extended into a quantitative setting. Here, we investigate weighted context-free languages of infinite words, a generalization of $\omega$-context-free…

We investigate the connection between properties of formal languages and properties of their generating series, with a focus on the class of holonomic power series. We first prove a strong version of a conjecture by Castiglione and…

Recently researchers working in the LFG framework have proposed algorithms for taking advantage of the implicit context-free components of a unification grammar [Maxwell 96]. This paper clarifies the mathematical foundations of these…

We study the computational complexity of reachability, coverability and inclusion for extensions of context-free commutative grammars with integer counters and reset operations on them. Those grammars can alternatively be viewed as an…

The introduction of Parikh matrices by Mateescu et al. in 2001 has sparked numerous new investigations in the theory of formal languages by various researchers, among whom is Serbanuta. Recently, a decade-old conjecture by Serbanuta on the…

Parikh automata extend finite automata by counters that can be tested for membership in a semilinear set, but only at the end of a run, thereby preserving many of the desirable algorithmic properties of finite automata. Here, we study the…

Parikh's Theorem is a fundamental result in automata theory with numerous applications in computer science: software verification (e.g. infinite-state verification, string constraints, and theory of arrays), verification of cryptographic…

We introduce a normal form for context-free grammars, called Dyck normal form. This is a syntactical restriction of the Chomsky normal form, in which the two nonterminals occurring on the right-hand side of a rule are paired nonterminals.…

Many formal languages include binders as well as operators that satisfy equational axioms, such as commutativity. Here we consider the nominal language, a general formal framework which provides support for the representation of binders,…

Parikh's theorem states that every Context Free Language (CFL) has the same Parikh image as that of a regular language. A finite state automaton accepting such a regular language is called a Parikh-equivalent automaton. In the worst case,…