Search results for "nonlinear"
showing 10 items of 3684 documents
Nonmalleable encryption of quantum information
2008
We introduce the notion of "non-malleability" of a quantum state encryption scheme (in dimension d): in addition to the requirement that an adversary cannot learn information about the state, here we demand that no controlled modification of the encrypted state can be effected. We show that such a scheme is equivalent to a "unitary 2-design" [Dankert et al.], as opposed to normal encryption which is a unitary 1-design. Our other main results include a new proof of the lower bound of (d^2-1)^2+1 on the number of unitaries in a 2-design [Gross et al.], which lends itself to a generalization to approximate 2-design. Furthermore, while in prime power dimension there is a unitary 2-design with =…
Probabilities to Accept Languages by Quantum Finite Automata
1999
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 hierarchy. These probabilities converge to 1/2.
Nondeterministic Moore automata and Brzozowski's minimization algorithm
2012
AbstractMoore automata represent a model that has many applications. In this paper we define a notion of coherent nondeterministic Moore automaton (NMA) and show that such a model has the same computational power of the classical deterministic Moore automaton. We consider also the problem of constructing the minimal deterministic Moore automaton equivalent to a given NMA. We propose an algorithm that is a variant of Brzozowski’s minimization algorithm in the sense that it is essentially structured as reverse operation and subset construction performed twice. Moreover, we explore more general classes of NMA and analyze the applicability of the algorithm. For some of such classes the algorith…
Standard Sturmian words and automata minimization algorithms
2015
The study of some close connections between the combinatorial properties of words and the performance of the automata minimization process constitutes the main focus of this paper. These relationships have been, in fact, the basis of the study of the tightness and the extremal cases of Hopcroft's algorithm, that is, up to now, the most efficient minimization method for deterministic finite state automata. Recently, increasing attention has been paid to another minimization method that, unlike the approach proposed by Hopcroft, is not based on refinement of the set of states of the automaton, but on automata operations such as determinization and reverse, and is also applicable to non-determ…
Group Input Machine
2009
We introduce a new type of internal memory for finite automata and real-time automata. Instead of using tapes with a prescribed Euclidean structure (one-dimensional or two-dimensional tapes) we allow arbitrary group structure of the internal memory of the automata.
Extremal minimality conditions on automata
2012
AbstractIn this paper we investigate the minimality problem of DFAs by varying the set of final states. In other words, we are interested on how the choice of the final states can affect the minimality of the automata. The state-pair graph is a useful tool to investigate such a problem. The choice of a set of final states for the automaton A defines a coloring of the closed components of the state-pair graph and the minimality of A corresponds to a property of these colored components. A particular attention is devoted to the analysis of some extremal cases such as, for example, the automata that are minimal for any choice of the subset of final states F from the state set Q of the automato…
Automata with Extremal Minimality Conditions
2010
It is well known that the minimality of a deterministic finite automaton (DFA) depends on the set of final states. In this paper we study the minimality of a strongly connected DFA by varying the set of final states. We consider, in particular, some extremal cases. A strongly connected DFA is called uniformly minimal if it is minimal, for any choice of the set of final states. It is called never-minimal if it is not minimal, for any choice of the set of final states. We show that there exists an infinite family of uniformly minimal automata and that there exists an infinite family of never-minimal automata. Some properties of these automata are investigated and, in particular, we consider t…
A graph theoretic approach to automata minimality
2012
AbstractThe paper presents a graph-theoretic approach to test the minimality of a deterministic automaton. In particular, we focus on problems concerning the dependence of the minimality of an automaton on the choice of the set F of final states or on the cardinality of the set F. We introduce different minimality conditions of an automaton and show that such conditions can be characterized in graph-theoretic terms.
Nondeterministic Moore Automata and Brzozowski’s Algorithm
2011
Moore automata represent a model that has many applications. In this paper we define a notion of coherent nondeterministic Moore automaton (NMA) and show that such a model has the same computational power of the classical deterministic Moore automaton. We consider also the problem of constructing the minimal deterministic Moore automaton equivalent to a given NMA. In this paper we propose an algorithm that is a variant of Brzozowski's algorithm in the sense that it is essentially structured as reverse operation and subset construction performed twice.
On Extremal Cases of Hopcroft’s Algorithm
2009
In this paper we consider the problem of minimization of deterministic finite automata (DFA) with reference to Hopcroft’s algorithm. Hopcroft’s algorithm has several degrees of freedom, so there can exist different sequences of refinements of the set of the states that lead to the final partition. We find an infinite family of binary automata for which such a process is unique. Some recent papers (cf. [3,7,1]) have been devoted to find families of automata for which Hopcroft’s algorithm has its worst execution time. They are unary automata associated to circular words. However, automata minimization can be achieved also in linear time when the alphabet has only one letter (cf. [14]), so in …