Search results for "non-deterministic"
showing 7 items of 7 documents
Positive Versions of Polynomial Time
1998
Abstract We show that restricting a number of characterizations of the complexity class P to be positive (in natural ways) results in the same class of (monotone) problems, which we denote by posP . By a well-known result of Razborov, posP is a proper subclass of the class of monotone problems in P . We exhibit complete problems for posP via weak logical reductions, as we do for other logically defined classes of problems. Our work is a continuation of research undertaken by Grigni and Sipser, and subsequently Stewart; indeed, we introduce the notion of a positive deterministic Turing machine and consequently solve a problem posed by Grigni and Sipser.
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…
Minimal nontrivial space complexity of probabilistic one- way turing machines
2005
Languages recognizable in o(log log n) space by probabilistic one — way Turing machines are proved to be regular. This solves an open problem in [4].
A description based on languages of the final non-deterministic automaton
2014
The study of the behaviour of non-deterministic automata has traditionally focused on the languages which can be associated to the different states. Under this interpretation, the different branches that can be taken at every step are ignored. However, we can also take into account the different decisions which can be made at every state, that is, the branches that can be taken, and these decisions might change the possible future behaviour. In this case, the behaviour of the automata can be described with the help of the concept of bisimilarity. This is the kind of description that is usually obtained when the automata are regarded as labelled transition systems or coalgebras. Contrarily t…
Quantum Real - Time Turing Machine
2001
The principles of quantum computation differ from the principles of classical computation very much. Quantum analogues to the basic constructions of the classical computation theory, such as Turing machine or finite 1-way and 2-ways automata, do not generalize deterministic ones. Their capabilities are incomparable. The aim of this paper is to introduce a quantum counterpart for real - time Turing machine. The recognition of a special kind of language, that can't be recognized by a deterministic real - time Turing machine, is shown.
Space-Efficient 1.5-Way Quantum Turing Machine
2001
1.5QTM is a sort of QTM (Quantum Turing Machine) where the head cannot move left (it can stay where it is and move right). For computations is used other - work tape. In this paper will be studied possibilities to economize work tape space more than the same deterministic Turing Machine can do (for some of the languages). As an example language (0i1i|i ≥ 0) is chosen, and is proved that this language could be recognized by deterministic Turing machine using log(i) cells on work tape , and 1.5QTM can recognize it using constant cells quantity.