Related papers: Formalization of the pumping lemma for context-fre…
Following a seminar the present author gave to an Automata Theory course to computer science students, it will be presented, in a very synthetic and mostly selfcontained way, the principal properties of context free languages (CFL), with…
Pumping lemmas are created to prove that given languages are not belong to certain language classes. There are several known pumping lemmas for the whole class and some special classes of the context-free languages. In this paper we prove…
The pumping lemma for context-free languages is a result about pushdown automata which is strikingly similar to the well-known pumping lemma for regular languages. However, though the lemma for regular languages is simply proved by using…
Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different tools are being increasingly used in…
Context-free grammar simplification is a subject of high importance in computer language processing technology as well as in formal language theory. This paper presents a formalization, using the Coq proof assistant, of the fact that…
In formal language theory, one of the most fundamental tools, known as pumping lemmas, is extremely useful for regular and context-free languages. However, there are natural properties for which the pumping lemmas are of little use. One of…
The pumping lemma and Ogden lemma offer a powerful method to prove that a particular language is not context-free. In 2008 Kanazawa proved an analogue of pumping lemma for well-nested multiple-context free languages. However, the statement…
Context-free language theory is a well-established area of mathematics, relevant to computer science foundations and technology. This paper presents the preliminary results of an ongoing formalization project using context-free grammars and…
Context-free language theory is a subject of high importance in computer language processing technology as well as in formal language theory. This paper presents a formalization, using the Coq proof assistant, of fundamental results related…
The paper is about a class of languages that extends context-free languages (CFL) and is stable under shuffle. Specifically, we investigate the class of partially-commutative context-free languages (PCCFL), where non-terminal symbols are…
We motivate and prove a strong pumping lemma for regular tree languages. The new lemma can be seen as the natural correspondent of Ogden's lemma for context-free string languages.
We present a necessary condition for an infinite language to be multiple context-free, which we call a Substitution Lemma. We apply it to show a sample selection of languages are not multiple context-free, including the word problem of the…
Pumping lemmata are the main tool to prove that a certain language does not belong to a class of languages like the recognizable languages or the context-free languages. Essentially two pumping lemmata exist for the recognizable weighted…
It is well-known that: (i) every context-free language over a singleton terminal alphabet is regular, and (ii) the class of languages that satisfy the Pumping Lemma is a proper super-class of the context-free languages. We show that any…
We study a pumping lemma for the word/tree languages generated by higher-order grammars. Pumping lemmas are known up to order-2 word languages (i.e., for regular/context-free/indexed languages), and have been used to show that a given…
In this article, we provide three coalgebraic characterizations of the class of context-free languages, each based on the idea of adding coalgebraic structure to an existing algebraic structure by specifying output-derivative pairs. Final…
We prove a kind of a pumping lemma for languages accepted by one-register alternating finite-memory automata. As a corollary, we obtain that the set of lengths of words in such languages is semi-linear.
Yamakami [2011, Theoret. Comput. Sci.] studies context-free languages with advice functions. Here, the length of an advice is assumed to be the same as that of an input. Let CFL and CFL/n denote the class of all context-free languages and…
To study quantum computation, it might be helpful to generalize structures from language and automata theory to the quantum case. To that end, we propose quantum versions of finite-state and push-down automata, and regular and context-free…
Context-free languages are widely used to describe the syntax of programming languages and natural languages. Usually, we describe a context-free language mathematically with the help of context-free grammar (for generation) or pushdown…