Related papers: Rule-weighted and terminal-weighted context-free g…
The present work analyzes the redundancy of sets of combinatorial objects produced by a weighted random generation algorithm proposed by Denise et al. This scheme associates weights to the terminals symbols of a weighted context-free…
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…
Many complex generative systems use languages to create structured objects. We consider a model of random languages, defined by weighted context-free grammars. As the distribution of grammar weights broadens, a transition is found from a…
Weighted automata model quantitative aspects of systems like the consumption of resources during executions. Traditionally, the weights are assumed to form the algebraic structure of a semiring, but recently also other weight computations…
We consider two models for the sequence labeling (tagging) problem. The first one is a {\em Pattern-Based Conditional Random Field }(\PB), in which the energy of a string (chain labeling) $x=x_1\ldots x_n\in D^n$ is a sum of terms over…
Context-free S grammars are introduced, for arbitrary (storage) type S, as a uniform framework for recursion-based grammars, automata, and transducers, viewed as programs. To each occurrence of a nonterminal of a context-free S grammar an…
Semantic word embeddings represent the meaning of a word via a vector, and are created by diverse methods. Many use nonlinear operations on co-occurrence statistics, and have hand-tuned hyperparameters and reweighting methods. This paper…
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…
Probabilistic context-free grammars have a long-term record of use as generative models in machine learning and symbolic regression. When used for symbolic regression, they generate algebraic expressions. We define the latter as equivalence…
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…
This paper solves an open problem concerning the generative power of nonerasing context-free rewriting systems using a simple mechanism for checking for context dependencies, in the literature known as semi-conditional grammars of degree…
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 propose a scalable framework for deciding, proving, and explaining (in-)equivalence of context-free grammars. We present an implementation of the framework and evaluate it on large data sets collected within educational support systems.…
We study a formalization of the grammar induction problem that models sentences as being generated by a compound probabilistic context-free grammar. In contrast to traditional formulations which learn a single stochastic grammar, our…
We study random words in a weighted regular language that achieve the maximal free energy using thermodynamics formalism. In particular, typical words in the language are algorithmically generated which have applications in computer…
Nested words, a model for recursive programs proposed by Alur and Madhusudan, have recently gained much interest. In this paper we introduce quantitative extensions and study nested word series which assign to nested words elements of a…
In this paper, we investigate the expressive power and the algorithmic properties of weighted expressions, which define functions from finite words to integers. First, we consider a slight extension of an expression formalism, introduced by…
It is known that hyperedge replacement grammars are similar to string context-free grammars in the sense of definitions and properties. Therefore, we expect that there is a generalization of the well-known Greibach normal form from string…
Asymptotic properties of finitely generated subgroups of free groups, and of finite group presentations, can be considered in several fashions, depending on the way these objects are represented and on the distribution assumed on these…
Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages~$L$ that assign to each word~$w$ a real number~$L(w)$. In the case of infinite words, the value of a run is…