37,887 research outputs found
Entanglement as a semantic resource
The characteristic holistic features of the quantum theoretic formalism and the intriguing notion of entanglement can be applied to a field that is far from microphysics: logical semantics. Quantum computational logics are new forms of quantum logic that have been suggested by the theory of quantum logical gates in quantum computation. In the standard semantics of these logics, sentences denote quantum information quantities: systems of qubits (quregisters) or, more generally, mixtures of quregisters (qumixes), while logical connectives are interpreted as special quantum logical gates (which have a characteristic reversible and dynamic behavior). In this framework, states of knowledge may be entangled, in such a way that our information about the whole determines our information about the parts; and the procedure cannot be, generally, inverted. In spite of its appealing properties, the standard version of the quantum computational semantics is strongly "Hilbert-space dependent". This certainly represents a shortcoming for all applications, where real and complex numbers do not generally play any significant role (as happens, for instance, in the case of natural and of artistic languages). We propose an abstract version of quantum computational semantics, where abstract qumixes, quregisters and registers are identified with some special objects (not necessarily living in a Hilbert space), while gates are reversible functions that transform qumixes into qumixes. In this framework, one can give an abstract definition of the notions of superposition and of entangled pieces of information, quite independently of any numerical values. We investigate three different forms of abstract holistic quantum computational logic
Descriptional complexity of cellular automata and decidability questions
We study the descriptional complexity of cellular automata (CA), a parallel model of computation. We show that between one of the simplest cellular models, the realtime-OCA. and "classical" models like deterministic finite automata (DFA) or pushdown automata (PDA), there will be savings concerning the size of description not bounded by any recursive function, a so-called nonrecursive trade-off. Furthermore, nonrecursive trade-offs are shown between some restricted classes of cellular automata. The set of valid computations of a Turing machine can be recognized by a realtime-OCA. This implies that many decidability questions are not even semi decidable for cellular automata. There is no pumping lemma and no minimization algorithm for cellular automata
Ciliate Gene Unscrambling with Fewer Templates
One of the theoretical models proposed for the mechanism of gene unscrambling
in some species of ciliates is the template-guided recombination (TGR) system
by Prescott, Ehrenfeucht and Rozenberg which has been generalized by Daley and
McQuillan from a formal language theory perspective. In this paper, we propose
a refinement of this model that generates regular languages using the iterated
TGR system with a finite initial language and a finite set of templates, using
fewer templates and a smaller alphabet compared to that of the Daley-McQuillan
model. To achieve Turing completeness using only finite components, i.e., a
finite initial language and a finite set of templates, we also propose an
extension of the contextual template-guided recombination system (CTGR system)
by Daley and McQuillan, by adding an extra control called permitting contexts
on the usage of templates.Comment: In Proceedings DCFS 2010, arXiv:1008.127
Preferential Multi-Context Systems
Multi-context systems (MCS) presented by Brewka and Eiter can be considered
as a promising way to interlink decentralized and heterogeneous knowledge
contexts. In this paper, we propose preferential multi-context systems (PMCS),
which provide a framework for incorporating a total preorder relation over
contexts in a multi-context system. In a given PMCS, its contexts are divided
into several parts according to the total preorder relation over them,
moreover, only information flows from a context to ones of the same part or
less preferred parts are allowed to occur. As such, the first preferred
parts of an PMCS always fully capture the information exchange between contexts
of these parts, and then compose another meaningful PMCS, termed the
-section of that PMCS. We generalize the equilibrium semantics for an MCS to
the (maximal) -equilibrium which represents belief states at least
acceptable for the -section of an PMCS. We also investigate inconsistency
analysis in PMCS and related computational complexity issues
Sublinearly space bounded iterative arrays
Iterative arrays (IAs) are a, parallel computational model with a sequential processing of the input. They are one-dimensional arrays of interacting identical deterministic finite automata. In this note, realtime-lAs with sublinear space bounds are used to accept formal languages. The existence of a proper hierarchy of space complexity classes between logarithmic anel linear space bounds is proved. Furthermore, an optimal spacc lower bound for non-regular language recognition is shown. Key words: Iterative arrays, cellular automata, space bounded computations, decidability questions, formal languages, theory of computatio
Graph-Controlled Insertion-Deletion Systems
In this article, we consider the operations of insertion and deletion working
in a graph-controlled manner. We show that like in the case of context-free
productions, the computational power is strictly increased when using a control
graph: computational completeness can be obtained by systems with insertion or
deletion rules involving at most two symbols in a contextual or in a
context-free manner and with the control graph having only four nodes.Comment: In Proceedings DCFS 2010, arXiv:1008.127
On the descriptional complexity of iterative arrays
The descriptional complexity of iterative arrays (lAs) is studied. Iterative arrays are a parallel computational model with a sequential processing of the input. It is shown that lAs when compared to deterministic finite automata or pushdown automata may provide savings in size which are not bounded by any recursive function, so-called non-recursive trade-offs. Additional non-recursive trade-offs are proven to exist between lAs working in linear time and lAs working in real time. Furthermore, the descriptional complexity of lAs is compared with cellular automata (CAs) and non-recursive trade-offs are proven between two restricted classes. Finally, it is shown that many decidability questions for lAs are undecidable and not semidecidable
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