Search results for "Machine"
showing 10 items of 2592 documents
Counting with Probabilistic and Ultrametric Finite Automata
2014
We investigate the state complexity of probabilistic and ultrametric finite automata for the problem of counting, i.e. recognizing the one-word unary language \(C_n=\left\{ 1^n \right\} \). We also review the known results for other types of automata.
Superiority Of One-Way And Realtime Quantum Machines
2012
In automata theory, quantum computation has been widely examined for finite state machines, known as quantum finite automata (QFAs), and less attention has been given to QFAs augmented with counters or stacks. In this paper, we focus on such generalizations of QFAs where the input head operates in one-way or realtime mode, and present some new results regarding their superiority over their classical counterparts. Our first result is about the nondeterministic acceptance mode: Each quantum model architecturally intermediate between realtime finite state automaton and one-way pushdown automaton (one-way finite automaton, realtime and one-way finite automata with one-counter, and realtime push…
Affine Automata Verifiers
2021
We initiate the study of the verification power of Affine finite automata (AfA) as a part of Arthur-Merlin (AM) proof systems. We show that every unary language is verified by a real-valued AfA verifier. Then, we focus on the verifiers restricted to have only integer-valued or rational-valued transitions. We observe that rational-valued verifiers can be simulated by integer-valued verifiers, and their protocols can be simulated in nondeterministic polynomial time. We show that this upper bound is tight by presenting an AfA verifier for NP-complete problem SUBSETSUM. We also show that AfAs can verify certain non-affine and non-stochastic unary languages.
Machine-Independent Characterizations and Complete Problems for Deterministic Linear Time
2002
This article presents two algebraic characterizations and two related complete problems for the complexity class DLIN that was introduced in [E. Grandjean, Ann. Math. Artif. Intell., 16 (1996), pp. 183--236]. DLIN is essentially the class of all functions that can be computed in linear time on a Random Access Machine which uses only numbers of linear value during its computations. The algebraic characterizations are in terms of recursion schemes that define unary functions. One of these schemes defines several functions simultaneously, while the other one defines only one function. From the algebraic characterizations, we derive two complete problems for DLIN under new, very strict, and mac…
A comparison of compatible, finite, and inductive graph properties
1993
Abstract In the theory of hyperedge-replacement grammars and languages, one encounters three types of graph properties that play an important role in proving decidability and structural results. The three types are called compatible, finite, and inductive graph properties. All three of them cover graph properties that are well-behaved with respect to certain operations on hypergraphs. In this paper, we show that the three notions are essentially equivalent. Consequently, three lines of investigation in the theory of hyperedge replacement - so far separated - merge into one.
A Logical Characterisation of Linear Time on Nondeterministic Turing Machines
1999
The paper gives a logical characterisation of the class NTIME(n) of problems that can be solved on a nondeterministic Turing machine in linear time. It is shown that a set L of strings is in this class if and only if there is a formula of the form ∃f1..∃fk∃R1..∃Rm∀xφv; that is true exactly for all strings in L. In this formula the fi are unary function symbols, the Ri are unary relation symbols and φv; is a quantifierfree formula. Furthermore, the quantification of functions is restricted to non-crossing, decreasing functions and in φv; no equations in which different functions occur are allowed. There are a number of variations of this statement, e.g., it holds also for k = 3. From these r…
Quantum Pushdown Automata
2000
Quantum finite automata, as well as quantum pushdown automata were first introduced by C. Moore, J. P. Crutchfield [13]. In this paper we introduce the notion of quantum pushdown automata (QPA) in a non-equivalent way, including unitarity criteria, by using the definition of quantum finite automata of [11]. It is established that the unitarity criteria of QPA are not equivalent to the corresponding unitarity criteria of quantum Turing machines [4]. We show that QPA can recognize every regular language. Finally we present some simple languages recognized by QPA, two of them are not recognizable by deterministic pushdown automata and one seems to be not recognizable by probabilistic pushdown …
Quantum Finite Multitape Automata
1999
Quantum finite automata were introduced by C. Moore, J. P. Crutchfield [4], and by A. Kondacs and J. Watrous [3]. This notion is not a generalization of the deterministic finite automata. Moreover, in [3] it was proved that not all regular languages can be recognized by quantum finite automata. A. Ambainis and R. Freivalds [1] proved that for some languages quantum finite automata may be exponentially more concise rather than both deterministic and probabilistic finite automata. In this paper we introduce the notion of quantum finite multitape automata and prove that there is a language recognized by a quantum finite automaton but not by deterministic or probabilistic finite automata. This …
Quantum Finite State Transducers
2001
We introduce quantum finite state transducers (qfst), and study the class of relations which they compute. It turns out that they share many features with probabilistic finite state transducers, especially regarding undecidability of emptiness (at least for low probability of success). However, like their 'little brothers', the quantum finite automata, the power of qfst is incomparable to that of their probabilistic counterpart. This we show by discussing a number of characteristic examples.
Improved constructions of quantum automata
2008
We present a simple construction of quantum automata which achieve an exponential advantage over classical finite automata. Our automata use \frac{4}{\epsilon} \log 2p + O(1) states to recognize a language that requires p states classically. The construction is both substantially simpler and achieves a better constant in the front of \log p than the previously known construction of Ambainis and Freivalds (quant-ph/9802062). Similarly to Ambainis and Freivalds, our construction is by a probabilistic argument. We consider the possibility to derandomize it and present some results in this direction.