Related papers: A short proof that $O_2$ is an MCFL
A linear ordering is called context-free if it is the lexicographic ordering of some context-free language and is called scattered if it has no dense subordering. Each scattered ordering has an associated ordinal, called its rank. It is…
We present a simple new method for proving that languages are not regular. We prove the correctness of the method, illustrate the ease of using the method on well-known examples of nonregular languages, and prove two additional theorems on…
This paper considers the word problem for free inverse monoids of finite rank from a language theory perspective. It is shown that no free inverse monoid has context-free word problem; that the word problem of the free inverse monoid of…
We give a Kleene-type operational characterization of Muller context-free languages (MCFLs) of well-ordered and scattered words.
The ability of Large Language Models (LLMs) to perform reasoning tasks such as deduction has been widely investigated in recent years. Yet, their capacity to generate proofs-faithful, human-readable explanations of why conclusions…
Regular word grammars are restricted context-free grammars that define all the recognizable languages of words. This paper generalizes regular grammars from words to certain classes of graphs, by defining regular grammars for unordered…
Multiple (simple) context-free tree grammars are investigated, where "simple" means "linear and nondeleting". Every multiple context-free tree grammar that is finitely ambiguous can be lexicalized; i.e., it can be transformed into an…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
Transformers excel empirically on tasks that process well-formed inputs according to some grammar, such as natural language and code. However, it remains unclear how they can process grammatical syntax. In fact, under standard complexity…
It is well-known that every first-order property on words is expressible using at most three variables. The subclass of properties expressible with only two variables is also quite interesting and well-studied. We prove precise structure…
We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the state-complexity of representing sub- or superword closures of context-free grammars (CFGs): (1) We prove a (tight) upper bound of $2^{\mathcal{O}(n)}$ on the size of…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
We prove in this paper that the length of the Wadge hierarchy of omega context free languages is greater than the Cantor ordinal epsilon_omega, which is the omega-th fixed point of the ordinal exponentiation of base omega. The same result…
In single-core processors, concurrency requires that multiple processes be interleaved into a single thread of execution by a scheduler. The language-theoretic operation that corresponds to this is the shuffle of two languages: the set of…
This paper presents a multidimensional Dependency Grammar (DG), which decouples the dependency tree from word order, such that surface ordering is not determined by traversing the dependency tree. We develop the notion of a \emph{word order…
An F-system is a computational model that performs a folding operation on words of a given language, following directions coded on words of another given language. This paper considers the case in which both given languages are regular, and…
Verification of properties of first order logic with two variables FO2 has been investigated in a number of contexts. Over arbitrary structures it is known to be decidable with NEXPTIME complexity, with finitely satisfiable formulas having…
There is a general phenomenon in algebra that numerous functors of homological significance admit characterization as derived limits of elementary functors defined over categories of free extensions. We demonstrate that upon restriction to…
This paper is the second in a series of three, the aim of which is to construct algebraic geometry over a free metabelian Lie algebra $F$. For the universal closure of free metabelian Lie algebra of finite rank $r \ge 2$ over a finite field…
One of the main reasons for the correspondence of regular languages and monadic second-order logic is that the class of regular languages is closed under images of surjective letter-to-letter homomorphisms. This closure property holds for…