Related papers: Exact Affine Counter Automata
Let $\mathcal{P}(\Sigma^*)$ be the semiring of languages, and consider its subset $\mathcal{P}(\Sigma)$. In this paper we define the language recognized by a weighted automaton over $\mathcal{P}(\Sigma)$ and a one-letter alphabet.…
Given a Probabilistic Finite Automata (PFA), a set of states S, and an error threshold e > 0, our algorithm approximates the infimum probability (quantifying over all infinite words) that the automata reaches S. Our result contrasts with…
Affine quantization is a parallel procedure to canonical quantization, which is ideally suited to deal with special problems. Vector affine quantization introduces multiple degrees of freedom which find that working together create novel…
The value 1 problem is a decision problem for probabilistic automata over finite words: given a probabilistic automaton A, are there words accepted by A with probability arbitrarily close to 1? This problem was proved undecidable recently.…
A study of assisted problem solving formalized via decompositions of deterministic finite automata is initiated. The landscape of new types of decompositions of finite automata this study uncovered is presented. Languages with various…
A Wheeler automaton is a finite state automaton whose states admit a total Wheeler order, reflecting the co-lexicographic order of the strings labeling source-to-node paths. A Wheeler language is a regular language admitting an accepting…
We introduce Merlin-Arthur (MA) automata where Merlin provides a certificate at the beginning of computation and it is scanned by Arthur before reading the input. We define Merlin-Arthur deterministic, probabilistic, and quantum finite…
We generalize some of the central results in automata theory to the abstraction level of coalgebras and thus lay out the foundations of a universal theory of automata operating on infinite objects. Let F be any set functor that preserves…
Deciding formulas mixing arithmetic and uninterpreted predicates is of practical interest, notably for applications in verification. Some decision procedures consist in building by structural induction an automaton that recognizes the set…
We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the…
Using a novel rewriting problem, we show that several natural decision problems about finite automata are undecidable (i.e., recursively unsolvable). In contrast, we also prove three related problems are decidable. We apply one result to…
History-deterministic automata are those in which nondeterministic choices can be correctly resolved stepwise: there is a strategy to select a continuation of a run given the next input letter so that if the overall input word admits some…
The store language of an automaton is the set of store configurations (state and store contents, but not the input) that can appear as an intermediate step in an accepting computation. A one-way nondeterministic finite-visit Turing machine…
For a given regular language of infinite trees, one can ask about the minimal number of priorities needed to recognize this language with a non-deterministic, alternating, or weak alternating parity automaton. These questions are known as,…
A recent paper by Drewes, Hoffmann, and Minas (GCM 2023 proceedings) has shown that certain graph languages can be defined and efficiently recognized by finite automata when strings over typed symbols are interpreted as graphs. This…
We introduce the well structured problem as the question of whether a model (here a counter machine) is well structured (here for the usual ordering on integers). We show that it is undecidable for most of the (Presburger-defined) counter…
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…
Combining ideas from distributed algorithms and alternating automata, we introduce a new class of finite graph automata that recognize precisely the languages of finite graphs definable in monadic second-order logic. By restricting…
We describe a physical implementation of a quantum finite automaton recognizing a well known family of periodic languages. The realization exploits the polarization degree of freedom of single photons and their manipulation through linear…
We consider probabilistic automata on infinite words with acceptance defined by parity conditions. We consider three qualitative decision problems: (i) the positive decision problem asks whether there is a word that is accepted with…