Related papers: Construction of rational expression from tree auto…
We present counting reward automata-a finite state machine variant capable of modelling any reward function expressible as a formal language. Unlike previous approaches, which are limited to the expression of tasks as regular languages, our…
Regular expressions are commonly understood in terms of their denotational semantics, that is, through formal languages -- the regular languages. This view is inductive in nature: two primitives are equivalent if they are constructed in the…
Dependency syntax represents the structure of a sentence as a tree composed of dependencies, i.e., directed relations between lexical units. While in its more general form any such tree is allowed, in practice many are not plausible or are…
We propose a hybrid architecture that integrates decision tree-based symbolic reasoning with the generative capabilities of large language models (LLMs) within a coordinated multi-agent framework. Unlike prior approaches that loosely couple…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
Language models trained on internet-scale data sets have shown an impressive ability to solve problems in Natural Language Processing and Computer Vision. However, experience is showing that these models are frequently brittle in unexpected…
Automata acceptance can, in several situations of interest, be captured game-theoretically via acceptance games. The existence of a winning strategy for Verifier then captures the existence of a winning run-tree of a given automaton over a…
In this paper, we look at an unambiguous version of Simon's forest factorization theorem, a very deep result which has wide connections in algebra, logic and automata. Given a morphism $\varphi$ from $\Sigma^+$ to a finite semigroup $S$, we…
Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…
We propose a large language model explainability technique for obtaining faithful natural language explanations by grounding the explanations in a reasoning process. When converted to a sequence of tokens, the outputs of the reasoning…
Students find their first course in Formal Languages and Automata Theory challenging. In addition to the development of formal arguments, most students struggle to understand nondeterministic computation models. In part, the struggle stems…
We give a computational interpretation to an abstract instance of Zorn's lemma formulated as a wellfoundedness principle in the language of arithmetic in all finite types. This is achieved through G\"odel's functional interpretation, and…
We introduce a neural network that represents sentences by composing their words according to induced binary parse trees. We use Tree-LSTM as our composition function, applied along a tree structure found by a fully differentiable natural…
Preparing exact and comprehensive word meaning explanations is one of the key steps in the process of monolingual dictionary writing. In standard methodology, the explanations need an expert lexicographer who spends a substantial amount of…
The theory of computation is based on abstract computing automata which can be classified into a three-class hierarchy: Finite Automata (FA), Push-down Automata (PDA) and the Turing Machines (TM). Each class corresponds to grammar/language…
With the recent advancements in deep learning, neural solvers have gained promising results in solving math word problems. However, these SOTA solvers only generate binary expression trees that contain basic arithmetic operators and do not…
The automatic generation of decision trees based on off-line reasoning on models of a domain is a reasonable compromise between the advantages of using a model-based approach in technical domains and the constraints imposed by embedded…
Reaction automata are a formal model that has been introduced to investigate the computing powers of interactive behaviors of biochemical reactions([14]). Reaction automata are language acceptors with multiset rewriting mechanism whose…
The development of mechanised language specification based on structured operational semantics, with applications to verified compilers and sound program analysis, requires huge effort. General theory and frameworks have been proposed to…
It is well known that for a given bottom-up tree automaton it can be decided whether or not there exists deterministic top-down tree automaton that recognized the same tree language. Recently it was claimed that such a decision can be…