Related papers: State Grammars with Stores
For any context-free grammar, we build a transition diagram, that is, a finite directed graph with labeled arcs, which describes the work of the grammar. This approach is new, and it is different from previously known graph models. We…
State and measurement tomography make assumptions about the experimental states or measurements. These assumptions are often not justified because state preparation and measurement errors are unavoidable in practice. Here we describe how…
We study language generation in the limit under bounded memory. In this task, a learner observes examples from an unknown target language one at a time and must eventually output only new valid examples. Prior work assumes access to the…
We introduce weighted regular tree grammars with storage as combination of (a) regular tree grammars with storage and (b) weighted tree automata over multioperator monoids. Each weighted regular tree grammar with storage generates a…
Finite state machines are widely used as a sound mathematical formalism that appropriately describes large scale, distributed and complex systems. Multiple interactions of finite state machines in complex systems are well captured by the…
Techniques for plan recognition under uncertainty require a stochastic model of the plan-generation process. We introduce Probabilistic State-Dependent Grammars (PSDGs) to represent an agent's plan-generation process. The PSDG language…
Measuring the quality of a generated sequence against a set of references is a central problem in many learning frameworks, be it to compute a score, to assign a reward, or to perform discrimination. Despite great advances in model…
Current syntactic theory limits the range of grammatical variation so severely that the logical problem of grammar learning is trivial. Yet, children exhibit characteristic stages in syntactic development at least through their sixth year.…
This work examines approaches to making computational models reversible. Broadly speaking, transforming a computational model into a reversible one, i.e. reversibilizing it, means extending its operational semantics conservatively in a way…
In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. In the past, two independent hierarchies have been obtained for external and internal…
A new breed of gated-linear recurrent neural networks has reached state-of-the-art performance on a range of sequence modeling problems. Such models naturally handle long sequences efficiently, as the cost of processing a new input is…
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…
A structural time series model additively decomposes into generative, semantically-meaningful components, each of which depends on a vector of parameters. We demonstrate that considering each generative component together with its vector of…
We consider backward stochastic differential equations (BSDE) with nonlinear generators typically of quadratic growth in the control variable. A measure solution of such a BSDE will be understood as a probability measure under which the…
Consider nondeterministic finite automata recognizing base-k positional notation of numbers. Assume that numbers are read starting from their least significant digits. It is proved that if two sets of numbers S and T are represented by…
We investigate the global GRAMMAR constraint over restricted classes of context free grammars like deterministic and unambiguous context-free grammars. We show that detecting disentailment for the GRAMMAR constraint in these cases is as…
We classify and re-examine some of the current approaches to improve the performance-computes trade-off of language models, including (1) non-causal models (such as masked language models), (2) extension of batch length with efficient…
Structured State Spaces for Sequences (S4) is a recently proposed sequence model with successful applications in various tasks, e.g. vision, language modeling, and audio. Thanks to its mathematical formulation, it compresses its input to a…
By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions…
We introduce stochastic and quantum finite-state transducers as computation-theoretic models of classical stochastic and quantum finitary processes. Formal process languages, representing the distribution over a process's behaviors, are…