Related papers: New results on classical and quantum counter autom…
Quantum finite automata have been studied intensively since their introduction in late 1990s as a natural model of a quantum computer with finite-dimensional quantum memory space. This paper seeks their direct application to interactive…
We first show that given a $k_1$-letter quantum finite automata $\mathcal{A}_1$ and a $k_2$-letter quantum finite automata $\mathcal{A}_2$ over the same input alphabet $\Sigma$, they are equivalent if and only if they are…
Parikh automata extend finite automata by counters that can be tested for membership in a semilinear set, but only at the end of a run, thereby preserving many of the desirable algorithmic properties of finite automata. Here, we study the…
In this note, we present an infinite family of promise problems which can be solved exactly by just tuning transition amplitudes of a two-state quantum finite automata operating in realtime mode, whereas the size of the corresponding…
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…
We study the power of quantum witnesses under perfect completeness. We construct a classical oracle relative to which a language lies in $\mathsf{QMA}_1$ but not in $\mathsf{QCMA}$ when the $\mathsf{QCMA}$ verifier is only allowed…
It is well known that quantum, randomized and deterministic (sequential) query complexities are polynomially related for total boolean functions. We find that significantly larger separations between the parallel generalizations of these…
Classical verification of quantum learning allows classical clients to reliably leverage quantum computing advantages by interacting with untrusted quantum servers. Yet, current quantum devices available in practice suffers from a variety…
The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied…
We show that bounded-error affine finite automata recognize uncountably many (and so some non-Turing recognizable) languages when using real-valued transitions.
Deterministic 2-head finite automata which are machines that process an input word from both ends are analyzed for their ability to perform reversible computations. This implies that the automata are backward deterministic, enabling unique…
We consider quantum-classical hybrid machine learning in which large-scale input channels remain classical and small-scale working channels process quantum operations conditioned on classical input data. This does not require the conversion…
Every language recognized by a non-deterministic finite automaton can be recognized by a deterministic automaton, at the cost of a potential increase of the number of states, which in the worst case can go from $n$ states to $2^n$ states.…
Kleene algebra axioms are complete with respect to both language models and binary relation models. In particular, two regular expressions recognise the same language if and only if they are universally equivalent in the model of binary…
We present a new decision procedure for the logic WS1S. It originates from the classical approach, which first builds an automaton accepting all models of a formula and then tests whether its language is empty. The main novelty is to test…
Using Albert results we argue that we don't need new physics to understand G\"odelization. Albert quantum automaton can "understand" both a formal system and a G\"odel proposition which can't be obtained within this system. There are two…
{\it Two-way finite automata with quantum and classical states} (2qcfa's) were introduced by Ambainis and Watrous. Though this computing model is more restricted than the usual {\it two-way quantum finite automata} (2qfa's) first proposed…
We show that the lambda-q calculus can efficiently simulate quantum Turing machines by showing how the lambda-q calculus can efficiently simulate a class of quantum cellular automaton that are equivalent to quantum Turing machines. We…
When used as verifiers in Arthur-Merlin systems, two-way quantum finite automata can verify membership in all languages with bounded error with double-exponential expected running time, which cannot be achieved by their classical…
We show that some results from the theory of group automata and monoid automata still hold for more general classes of monoids and models. Extending previous work for finite automata over commutative groups, we demonstrate a context-free…