Related papers: Pumping lemmas for linear and nonlinear context-fr…
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…
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…
Context-free languages (CFLs) are highly important in computer language processing technology as well as in formal language theory. The Pumping Lemma is a property that is valid for all context-free languages, and is used to show 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…
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…
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.
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…
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.
Geometric folding processes are ubiquitous in natural systems ranging from protein biochemistry to patterns of insect wings and leaves. In a previous study, a folding operation between strings of formal languages was introduced as a model…
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…
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…
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…
We present pumping lemmas for five classes of functions definable by fragments of weighted automata over the min-plus semiring, the max-plus semiring and the semiring of natural numbers. As a corollary we show that the hierarchy of…
These lecture notes are intended as a supplement to Moore and Mertens' The Nature of Computation or as a standalone resource, and are available to anyone who wants to use them. Comments are welcome, and please let me know if you use these…
We study the computational complexity of finite intersections and finite unions of deterministic context-free (dcf) languages. Earlier, Wotschke [J. Comput. System Sci. 16 (1978) 456--461] demonstrated that intersections of $(d+1)$ dcf…
Context-free languages can be characterized in several ways. This article studies projective linearisations of languages of simple dependency trees, i.e., dependency trees in which a node can govern at most one node with a given syntactic…
The study of the operational complexity of minimal pumping constants started in [J. DASSOW and I. JECKER. Operational complexity and pumping lemmas. Acta Inform., 59:337-355, 2022], where an almost complete picture of the operational…
We continue the research on the generative capacity of contextual grammars where contexts are adjoined around whole words (externally) or around subwords (internally) which belong to special regular selection languages. All languages…