相关论文: The Power of a Single Qubit: Two-way Quantum Finit…

In a recent paper we have described an optical implementation of a measure-once one-way quantum finite automaton recognizing a well-known family of unary periodic languages, accepting words not in the language with a given error…

Affine automata provide a finite-state computational model that preserves the linear-algebraic structure of quantum computation while operating entirely over the reals. Recent work has shown that affine automata can far surpass classical…

Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of…

Polynomial--time constant--space quantum Turing machines (QTMs) and logarithmic--space probabilistic Turing machines (PTMs) recognize uncountably many languages with bounded error (Say and Yakary\i lmaz 2014, arXiv:1411.7647). In this…

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…

This paper explains how any nondeterministic automaton for a regular language $L$ gives rise to a one-dimensional oriented Topological Quantum Field Theory (TQFT) with inner endpoints and zero-dimensional defects labelled by letters of the…

Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are…

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…

Although quantum computers are capable of solving problems like factoring exponentially faster than the best-known classical algorithms, determining the resources responsible for their computational power remains unclear. An important class…

We consider the so-called measure once finite quantum automata model introduced by Moore and Crutchfield in 2000. We show that given a language recognized by such a device and a linear context-free language, it is recursively decidable…

An automaton is partially ordered if the only cycles in its transition diagram are self-loops. The expressivity of partially ordered NFAs (poNFAs) can be characterized by the Straubing-Th\'erien hierarchy. Level 3/2 is recognized by poNFAs,…

We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathfrak{C}$ be a class of polynomial-size concepts, and suppose that $\mathfrak{C}$ can be PAC-learned with…

Polynomial-time quantum Turing machines are provably superior to their classical counterparts within a common space bound in $o(\log \log n)$. For $\Omega(\log \log n)$ space, the only known quantum advantage result has been the fact…

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 examine the characteristic features of reversible and quantum computations in the presence of supplementary external information, known as advice. In particular, we present a simple, algebraic characterization of languages recognized by…

We present upper and lower bounds of the computational complexity of the two-way communication model of multiple-prover quantum interactive proof systems whose verifiers are limited to measure-many two-way quantum finite automata. We prove…

In the literature, there exist several interesting hybrid models of finite automata which have both quantum and classical states. We call them semi-quantum automata. In this paper, we compare the descriptional power of these models with…

Partially ordered automata are automata where the transition relation induces a partial order on states. The expressive power of partially ordered automata is closely related to the expressivity of fragments of first-order logic on finite…

Quantitative Bipolar Argumentation Frameworks (QBAFs) provide an alternative approach to computing argument acceptability in Bipolar Argumentation Frameworks (BAFs). Each argument is assigned an initial strength, which is then updated to a…

The communication matrix for two-way deterministic finite automata (2DFA) with $n$ states is defined for an automaton over a full alphabet of all $(2n+1)^n$ possible symbols: its rows and columns are indexed by strings, and the entry $(u,…