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Large Language Models (LLMs) are huge artificial neural networks which primarily serve to generate text, but also provide a very sophisticated probabilistic model of language use. Since generating a semantically consistent text requires a…
This work is concerned with regular languages defined over large alphabets, either infinite or just too large to be expressed enumeratively. We define a generic model where transitions are labeled by elements of a finite partition of the…
We consider two natural problems about nondeterministic finite automata. First, given such an automaton M of n states, and a length l, does M accept a word of length l? We show that the classic problem of triangle-free graph recognition…
We present an algorithm to learn a deterministic timed automaton (DTA) via membership and equivalence queries. Our algorithm is an extension of the L* algorithm with a Myhill-Nerode style characterization of recognizable timed languages,…
Instruction-tuning language models has become a crucial step in aligning them for general use. Typically, this process involves extensive training on large datasets, incurring high training costs. In this paper, we introduce a novel…
Combinatorial samplers are algorithmic schemes devised for the approximate- and exact-size generation of large random combinatorial structures, such as context-free words, various tree-like data structures, maps, tilings, RNA molecules.…
While finite automata have minimal DFAs as a simple and natural normal form, deterministic omega-automata do not currently have anything similar. One reason for this is that a normal form for omega-regular languages has to speak about more…
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…
Morphisms to finite semigroups can be used for recognizing omega-regular languages. The so-called strongly recognizing morphisms can be seen as a deterministic computation model which provides minimal objects (known as the syntactic…
Automata expressiveness is an essential feature in understanding which of the formalisms available should be chosen for modelling a particular problem. Probabilistic and stochastic automata are suitable for modelling systems exhibiting…
The problem of inclusion of the language accepted by timed automaton $A$ (e.g., the implementation) in the language accepted by $B$ (e.g., the specification) is, in general, undecidable in the class of non-deterministic timed automata. In…
The classic approaches to synthesize a reactive system from a linear temporal logic (LTL) specification first translate the given LTL formula to an equivalent omega-automaton and then compute a winning strategy for the corresponding…
We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear Dynamic Logic (LDL) by temporal operators equipped with parameters that bound their scope. LDL itself was proposed as an extension of Linear Temporal Logic (LTL) that…
Large Language Models (LLMs) have transformed text generation through inherently probabilistic context-aware mechanisms, mimicking human natural language. In this paper, we systematically investigate the performance of various LLMs when…
Recently data trees and data words have received considerable amount of attention in connection with XML reasoning and system verification. These are trees or words that, in addition to labels from a finite alphabet, carry data values from…
Minimizing the size of finite automata is a fundamental problem in theoretical computer science. Beyond standard minimization, further reductions can be achieved by decomposing an automaton into smaller components whose languages combine…
Algorithm selection, a critical process of automated machine learning, aims to identify the most suitable algorithm for solving a specific problem prior to execution. Mainstream algorithm selection techniques heavily rely on problem…
We present a framework for obtaining effective characterizations of simple fragments of future temporal logic (LTL) with the natural numbers as time domain. The framework is based on a form of strongly unambiguous automata, also known as…
This article proposes novel off-line test generation techniques from non-deterministic timed automata with inputs and outputs (TAIOs) in the formal framework of the tioco conformance theory. In this context, a first problem is the…
We present a unified translation of LTL formulas into deterministic Rabin automata, limit-deterministic B\"uchi automata, and nondeterministic B\"uchi automata. The translations yield automata of asymptotically optimal size (double or…