Related papers: Register automata with linear arithmetic
In this paper we present a new dataset and user simulator e-QRAQ (explainable Query, Reason, and Answer Question) which tests an Agent's ability to read an ambiguous text; ask questions until it can answer a challenge question; and explain…
Let p/q be a rational number. Numeration in base p/q is defined by a function that evaluates each finite word over A_p={0,1,...,p-1} to some rational number. We let N_p/q denote the image of this evaluation function. In particular, N_p/q…
We propose a new extension of higher-order pushdown automata, which allows to use an infinite alphabet. The new automata recognize languages of data words (instead of normal words), which beside each its letter from a finite alphabet have a…
In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are…
A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA $N$, there exists a process algebraic term $p$ such that its semantics is…
A regular path query (RPQ) is a regular expression q that returns all node pairs (u, v) from a graph database that are connected by an arbitrary path labelled with a word from L(q). The obvious algorithmic approach to RPQ-evaluation (called…
This paper outlines new paradigms for real analysis and computability theory in the recently proposed non-Aristotelian finitary logic (NAFL). Constructive real analysis in NAFL (NRA) is accomplished by a translation of diagrammatic concepts…
Recent advancements in QA with LLM, like GPT-4, have shown limitations in handling complex multi-hop queries. We propose AT-RAG, a novel multistep RAG incorporating topic modeling for efficient document retrieval and reasoning. Using…
We study complexity of the model-checking problems for LTL with registers (also known as freeze LTL) and for first-order logic with data equality tests over one-counter automata. We consider several classes of one-counter automata (mainly…
Most existing end-to-end Table Question Answering (Table QA) models consist of a two-stage framework with a retriever to select relevant table candidates from a corpus and a reader to locate the correct answers from table candidates. Even…
We consider a general class of decision problems concerning formal languages, called ``(one-dimensional) unboundedness predicates'', for automata that feature reversal-bounded counters (RBCA). We show that each problem in this class reduces…
We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language -- the input of the problem -- and fixed language called filter is non-empty. We consider two kind of…
Nominal automata models serve as a formalism for data languages, and in fact often relate closely to classical register models. The paradigm of name allocation in nominal automata helps alleviate the pervasive computational hardness of…
We develop a behavioural theory of reflective parallel algorithms (RAs), i.e. synchronous parallel algorithms that can modify their own behaviour. The theory comprises a set of postulates defining the class of RAs, an abstract machine…
We are lifting classical problems from single instances to regular sets of instances. The task of finding a positive instance of the combinatorial problem $P$ in a potentially infinite given regular set is equivalent to the so called…
We introduce homing vector automata, which are finite automata augmented by a vector that is multiplied at each step by a matrix determined by the current transition, and have to return the vector to its original setting in order to accept…
We introduce the Neural State Machine, seeking to bridge the gap between the neural and symbolic views of AI and integrate their complementary strengths for the task of visual reasoning. Given an image, we first predict a probabilistic…
Motivated by the successful application of the theory of regular languages to formal verification of finite-state systems, there is a renewed interest in developing a theory of analyzable functions from strings to numerical values that can…
Let L be an infinite regular language on a totally ordered alphabet (A,<). Feeding a finite deterministic automaton (with output) with the words of L enumerated lexicographically with respect to < leads to an infinite sequence over the…
We present five examples where quantum finite automata (QFAs) outperform their classical counterparts. This may be useful as a relatively simple technique to introduce quantum computation concepts to computer scientists. We also describe a…