146,815 research outputs found
Instruction sequence processing operators
Instruction sequence is a key concept in practice, but it has as yet not come
prominently into the picture in theoretical circles. This paper concerns
instruction sequences, the behaviours produced by them under execution, the
interaction between these behaviours and components of the execution
environment, and two issues relating to computability theory. Positioning
Turing's result regarding the undecidability of the halting problem as a result
about programs rather than machines, and taking instruction sequences as
programs, we analyse the autosolvability requirement that a program of a
certain kind must solve the halting problem for all programs of that kind. We
present novel results concerning this autosolvability requirement. The analysis
is streamlined by using the notion of a functional unit, which is an abstract
state-based model of a machine. In the case where the behaviours exhibited by a
component of an execution environment can be viewed as the behaviours of a
machine in its different states, the behaviours concerned are completely
determined by a functional unit. The above-mentioned analysis involves
functional units whose possible states represent the possible contents of the
tapes of Turing machines with a particular tape alphabet. We also investigate
functional units whose possible states are the natural numbers. This
investigation yields a novel computability result, viz. the existence of a
universal computable functional unit for natural numbers.Comment: 37 pages; missing equations in table 3 added; combined with
arXiv:0911.1851 [cs.PL] and arXiv:0911.5018 [cs.LO]; introduction and
concluding remarks rewritten; remarks and examples added; minor error in
proof of theorem 4 correcte
A thread calculus with molecular dynamics
We present a theory of threads, interleaving of threads, and interaction
between threads and services with features of molecular dynamics, a model of
computation that bears on computations in which dynamic data structures are
involved. Threads can interact with services of which the states consist of
structured data objects and computations take place by means of actions which
may change the structure of the data objects. The features introduced include
restriction of the scope of names used in threads to refer to data objects.
Because that feature makes it troublesome to provide a model based on
structural operational semantics and bisimulation, we construct a projective
limit model for the theory.Comment: 47 pages; examples and results added, phrasing improved, references
replace
Further Results on the Power of Generating APCol Systems
In this paper we continue our investigations in APCol systems (Automatonlike
P colonies), variants of P colonies where the environment of the agents is given by a
string and the functioning of the system resembles to the functioning of standard nite
automaton. We rst deal with the concept of determinism in these systems and compare
deterministic APCol systems with deterministic register machines. Then we focus on
generating non-deterministic APCol systems with only one agent. We show that these
systems are as powerful as 0-type grammars, i.e., generate any recursively enumerable
language. If the APCol system is non-erasing, then any context-sensitive language can
be generated by a non-deterministic APCol systems with only one agent
On the behaviours produced by instruction sequences under execution
We study several aspects of the behaviours produced by instruction sequences
under execution in the setting of the algebraic theory of processes known as
ACP. We use ACP to describe the behaviours produced by instruction sequences
under execution and to describe two protocols implementing these behaviours in
the case where the processing of instructions takes place remotely. We also
show that all finite-state behaviours considered in ACP can be produced by
instruction sequences under execution.Comment: 36 pages, consolidates material from arXiv:0811.0436 [cs.PL],
arXiv:0902.2859 [cs.PL], and arXiv:0905.2257 [cs.PL]; abstract and
introduction rewritten, examples and proofs adde
Entanglement in Valence-Bond-Solid States
This article reviews the quantum entanglement in Valence-Bond-Solid (VBS)
states defined on a lattice or a graph. The subject is presented in a
self-contained and pedagogical way. The VBS state was first introduced in the
celebrated paper by I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki
(abbreviation AKLT is widely used). It became essential in condensed matter
physics and quantum information (measurement-based quantum computation). Many
publications have been devoted to the subject. Recently entanglement was
studied in the VBS state. In this review we start with the definition of a
general AKLT spin chain and the construction of VBS ground state. In order to
study entanglement, a block subsystem is introduced and described by the
density matrix. Density matrices of 1-dimensional models are diagonalized and
the entanglement entropies (the von Neumann entropy and Renyi entropy) are
calculated. In the large block limit, the entropies also approach finite
limits. Study of the spectrum of the density matrix led to the discovery that
the density matrix is proportional to a projector.Comment: Published version, 80 pages, 8 figures; references update
Towards composition of verified hardware devices
Computers are being used where no affordable level of testing is adequate. Safety and life critical systems must find a replacement for exhaustive testing to guarantee their correctness. Through a mathematical proof, hardware verification research has focused on device verification and has largely ignored system composition verification. To address these deficiencies, we examine how the current hardware verification methodology can be extended to verify complete systems
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