Related papers: Marciani Normal Form of context-free grammars
We continue our study of ordered context-free grammars, a grammar formalism that places an order on the parse trees produced by the corresponding context-free grammar. In particular, we simplify our previous definition of a derivation of a…
A recent study on structural properties of regular and context-free languages has greatly promoted our basic understandings of the complex behaviors of those languages. We continue the study to examine how regular languages behave when they…
Let $G$ be a finitely generated group, $A$ a finite set of generators and $K$ a subgroup of $G$. We call the pair $(G,K)$ context-free if the set of all words over $A$ that reduce in $G$ to an element of $K$ is a context-free language. When…
We consider languages generated by weighted context-free grammars. It is shown that the behaviour of large texts is controlled by saddle-point equations for an appropriate generating function. We then consider ensembles of grammars, in…
Linguistic evaluations of how well LMs generalize to produce or understand language often implicitly take for granted that natural languages are generated by symbolic rules. According to this perspective, grammaticality is determined by…
This paper studies the classes of semigoups and monoids with context-free and deterministic context-free word problem. First, some examples are exhibited to clarify the relationship between these classes and their connection with the…
During the last decades, classical models in language theory have been extended by control mechanisms defined by monoids. We study which monoids cause the extensions of context-free grammars, finite automata, or finite state transducers to…
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…
We present a new proof that $O_2$ is a multiple context-free language. It contrasts with a recent proof by Salvati (2015) in its avoidance of concepts that seem specific to two-dimensional geometry, such as the complex exponential function.…
Although adequate models of human language for syntactic analysis and semantic interpretation are of at least context-free complexity, for applications such as speech processing in which speed is important finite-state models are often…
We study the problem of computing the probability that a given stochastic context-free grammar (SCFG), G, generates a string in a given regular language L(D) (given by a DFA, D). This basic problem has a number of applications in…
A major target of linguistics and cognitive science has been to understand what class of learning systems can acquire the key structures of natural language. Until recently, the computational requirements of language have been used to argue…
This paper presents a restricted form of linear indexed grammars, called even linear indexed grammars, which yield the even linear indexed languages. These languages properly contain the context-free languages and are contained in the set…
A new family of categorial grammars is proposed, defined by enriching basic categorial grammars with a conjunction operation. It is proved that the formalism obtained in this way has the same expressive power as conjunctive grammars, that…
This paper explores two separate questions: Can we perform natural language processing tasks without a lexicon?; and, Should we? Existing natural language processing techniques are either based on words as units or use units such as grams…
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…
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
Classifying formal languages according to the expressiveness of grammars able to generate them is a fundamental problem in computational linguistics and, therefore, in the theory of computation. Furthermore, such kind of analysis can give…
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…
A finitely generated group $G$ is called poly-context-free if its word problem $\mathrm{WP}(G)$ is an intersection of finitely many context-free languages. We consider the quaternionic lattices $\Gamma_\tau$ over the field…