相关论文: Rational stochastic languages

Iverson's APL and its descendants (such as J, K and FISh) are examples of the family of "rank-polymorphic" programming languages. The principal control mechanism of such languages is the general lifting of functions that operate on arrays…

Semiautomata form a rich class of sequence-processing algorithms with applications in natural language processing, robotics, computational biology, and data mining. We establish the first Statistical Query hardness result for semiautomata…

A semilinear relation is a finite union of finite intersections of open and closed half-spaces over, for instance, the reals, the rationals, or the integers. Semilinear relations have been studied in connection with algebraic geometry,…

Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Stochastic acceptors or probabilistic automata are stochastic automata without output that can model components in machine learning…

Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are…

We propose a novel automata model over the alphabet of rational numbers, which we call register automata over the rationals (RA-Q). It reads a sequence of rational numbers and outputs another rational number. RA-Q is an extension of the…

We relate two measures of complexity of regular languages. The first is syntactic complexity, that is, the cardinality of the syntactic semigroup of the language. That semigroup is isomorphic to the semigroup of transformations of states…

Human language has a distinct systematic structure, where utterances break into individually meaningful words which are combined to form phrases. We show that natural-language-like systematicity arises in codes that are constrained by a…

Linguistic variables represent crisp information in a form and precision appropriate for the problem. For example, to answer the question "How are you?" one may say "I am fine." the linguistic variables like "fine", so common in everyday…

The syntactic complexity of a regular language is the size of its syntactic semigroup. This semigroup is isomorphic to the transition semigroup of the minimal deterministic finite automaton accepting the language, that is, to the semigroup…

Synchronous languages are now a standard industry tool for critical embedded systems. Designers write high-level specifications by composing streams of values using block diagrams. These languages have been extended with Bayesian reasoning…

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…

Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability…

In this work, it is proved that a set of numbers closed under addition and whose representations in a rational base numeration system is a rational language is not a finitely generated additive monoid. A key to the proof is the definition…

The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…

These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…

One of the fundamental open questions in computational complexity is whether the class of problems solvable by use of stochasticity under the Random Polynomial time (RP) model is larger than the class of those solvable in deterministic…

The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is…

Figurative language (e.g., irony, hyperbole, understatement) is ubiquitous in human communication, resulting in utterances where the literal and the intended meanings do not match. The Rational Speech Act (RSA) framework, which explicitly…

Coordination is a desirable feature in many multi-agent systems such as robotic and socioeconomic networks. We consider a task allocation problem as a binary networked coordination game over an undirected regular graph. Each agent in the…