Related papers: Quantitative Automata under Probabilistic Semantic…
We study the following decision problem: is the language recognized by a quantum finite automaton empty or non-empty? We prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or non-strict…
We study alternating automata with qualitative semantics over infinite binary trees: alternation means that two opposing players construct a decoration of the input tree called a run, and the qualitative semantics says that a run of the…
We study the determinisation and unambiguisation problems of weighted automata over the rational field: Given a weighted automaton, can we determine whether there exists an equivalent deterministic, respectively unambiguous, weighted…
Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages~$L$ that assign to each word~$w$ a real number~$L(w)$. In the case of infinite words, the value of a run is…
Complexity classes such as $\#\mathbf{P}$, $\oplus\mathbf{P}$, $\mathbf{GapP}$, $\mathbf{OptP}$, $\mathbf{NPMV}$, or the class of fuzzy languages realised by polynomial-time fuzzy nondeterministic Turing machines, can all be described in…
This paper introduces and investigates decision problems for numberless probabilistic automata, i.e. probabilistic automata where the support of each probabilistic transitions is specified, but the exact values of the probabilities are not.…
We introduce notions of simulation between semiring-weighted automata as models of quantitative systems. Our simulations are instances of the categorical/coalgebraic notions previously studied by Hasuo---hence soundness against language…
In probabilistic programming, the inference problem asks to determine a program's posterior distribution conditioned on its "observe" instructions. Inference is challenging, especially when exact rather than approximate results are…
Quantitative automata are useful representations for numerous applications, including modeling probability distributions over sequences to Markov chains and reward machines. Actively learning such automata typically occurs using explicitly…
Quantitative automata (QAs) extend finite-state automata on infinite words with weighted transitions to specify quantitative system properties. However, their finite weight sets rule out properties like average response time, where response…
Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages $L$ that assign to each word $w$ a real number $L(w)$. In the case of infinite words, the value of a run is…
A notion of alternating timed automata is proposed. It is shown that such automata with only one clock have decidable emptiness problem over finite words. This gives a new class of timed languages which is closed under boolean operations…
We prove that endowing a real-time probabilistic or quantum computer with the ability of postselection increases its computational power. For this purpose, we provide a new model of finite automata with postselection, and compare it with…
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.…
These lecture notes are intended as a supplement to Moore and Mertens' The Nature of Computation or as a standalone resource, and are available to anyone who wants to use them. Comments are welcome, and please let me know if you use these…
A featured transition system is a transition system in which the transitions are annotated with feature expressions: Boolean expressions on a finite number of given features. Depending on its feature expression, each individual transition…
The notion of comparison between system runs is fundamental in formal verification. This concept is implicitly present in the verification of qualitative systems, and is more pronounced in the verification of quantitative systems. In this…
This set of notes re-proves known results on weighted automata (over a field, also known as multiplicity automata). The text offers a unified view on theorems and proofs that have appeared in the literature over decades and were written in…
The question of whether quantum real-time one-counter automata (rtQ1CAs) can outperform their probabilistic counterparts has been open for more than a decade. We provide an affirmative answer to this question, by demonstrating a…
This paper offers a natural stochastic semantics of Networks of Priced Timed Automata (NPTA) based on races between components. The semantics provides the basis for satisfaction of probabilistic Weighted CTL properties (PWCTL),…