Related papers: Quantum Pushdown Automata
We give a one-dimensional quantum cellular automaton (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any one-dimensional QCA can be encoded within the initial…
There are many types of automata and grammar models that have been studied in the literature, and for these models, it is common to determine whether certain problems are decidable. One problem that has been difficult to answer throughout…
We present a language $L_n$ which is recognizable by a probabilistic finite automaton (PFA) with probability $1 - \epsilon$ for all $\epsilon > 0$ with $O(log^2n)$ states, with a deterministic finite automaton (DFA) with O(n) states, but a…
In this paper we study a generalized model named one-way general quantum finite automata} (1gQFA), in which each symbol in the input alphabet induces a trace-preserving quantum operation, instead of a unitary transformation. Two different…
We define a new subclass of nondeterministic finite automata for prefix-closed languages called Flanked Finite Automata (FFA). We show that this class enjoys good complexity properties while preserving the succinctness of nondeterministic…
We construct zero-error quantum finite automata (QFAs) for promise problems which cannot be solved by bounded-error probabilistic finite automata (PFAs). Here is a summary of our results: - There is a promise problem solvable by an exact…
We present a framework for the implementation of quantum finite automata algorithms designed for the language $ MOD_p = \{ a^{i\cdot p } \mid i \geq 0 \}$ on gate-based quantum computers. First, we compile the known theoretical results from…
System behaviors are traditionally evaluated through binary classifications of correctness, which do not suffice for properties involving quantitative aspects of systems and executions. Quantitative automata offer a more nuanced approach,…
Discretizing spacetime is often a natural step towards modelling physical systems. For quantum systems, if we also demand a strict bound on the speed of information propagation, we get quantum cellular automata (QCAs). These originally…
One-dimensional quantum cellular automata (QCA) consist in a line of identical, finite dimensional quantum systems. These evolve in discrete time steps according to a local, shift-invariant unitary evolution. By local we mean that no…
The standard inputs given to a quantum machine are classical binary strings. In this view, any quantum complexity class is a collection of subsets of $\{0,1\}^{*}$. However, a quantum machine can also accept quantum states as its input. T.…
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…
There have been several non-axiomatic approaches taken to define Quantum Cellular Automata (QCA). Partitioned QCA (PQCA) are the most canonical of these non-axiomatic definitions. In this work we first show that any QCA can be put into the…
The problem if a given configuration of a pushdown automaton (PDA) is bisimilar with some (unspecified) finite-state process is shown to be decidable. The decidability is proven in the framework of first-order grammars, which are given by…
To advance our understanding of Quantum Cellular Automata in problem solving through parallel and distributed computing, this research quantized the density classification problem and adopted the Quantum Particle Automata (QPA) to solve the…
Parikh automata on finite words were first introduced by Klaedtke and Rue{\ss} [Automata, Languages and Programming, 2003]. In this paper, we introduce several variants of Parikh automata on infinite words and study their expressiveness. We…
Probabilistic B\"uchi Automata (PBA) are randomized, finite state automata that process input strings of infinite length. Based on the threshold chosen for the acceptance probability, different classes of languages can be defined. In this…
We study 1-way quantum finite automata (QFAs) and compare them with their classical counterparts. We show that 1-way QFAs can be very space efficient. We construct a 1-way QFAs that are quadratically smaller than any equivalent…
We continue the systematic investigation of probabilistic and quantum finite automata (PFAs and QFAs) on promise problems by focusing on unary languages. We show that bounded-error QFAs are more powerful than PFAs. But, in contrary to the…
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…