50,998 research outputs found
State machines for large scale computer software and systems
A method for specifying the behavior and architecture of discrete state
systems such as digital electronic devices and software using deterministic
state machines and automata products. The state machines are represented by
sequence maps where indicates that the output of the
system is in the state reached by following the sequence of events from
the initial state. Examples provided include counters, networks, reliable
message delivery, real-time analysis of gates and latches, and
producer/consumer. Techniques for defining, parameterizing, characterizing
abstract properties, and connecting sequence functions are developed. Sequence
functions are shown to represent (possibly non-finite) Moore type state
machines and general products of state machines. The method draws on state
machine theory, automata products, and recursive functions and is ordinary
working mathematics, not involving formal methods or any foundational or
meta-mathematical techniques. Systems in which there are levels of components
that may operate in parallel or concurrently are specified in terms of function
composition
A Behavioural Theory of Recursive Algorithms
"What is an algorithm?" is a fundamental question of computer science.
Gurevich's behavioural theory of sequential algorithms (aka the sequential ASM
thesis) gives a partial answer by defining (non-deterministic) sequential
algorithms axiomatically, without referring to a particular machine model or
programming language, and showing that they are captured by (non-deterministic)
sequential Abstract State Machines (nd-seq ASMs). Moschovakis pointed out that
recursive algorithms such as mergesort are not covered by this theory. In this
article we propose an axiomatic definition of the notion of sequential
recursive algorithm which extends Gurevich's axioms for sequential algorithms
by a Recursion Postulate and allows us to prove that sequential recursive
algorithms are captured by recursive Abstract State Machines, an extension of
nd-seq ASMs by a CALL rule. Applying this recursive ASM thesis yields a
characterization of sequential recursive algorithms as finitely composed
concurrent algorithms all of whose concurrent runs are partial-order runs.Comment: 34 page
On the Equivalence between Small-Step and Big-Step Abstract Machines: A Simple Application of Lightweight Fusion
We show how Ohori and Sasano's recent lightweight fusion by fixed-point promotion provides a simple way to prove the equivalence of the two standard styles of specification of abstract machines: (1) in small-step form, as a state-transition function together with a `driver loop,' i.e., a function implementing the iteration of this transition function; and (2) in big-step form, as a tail-recursive function that directly maps a given configuration to a final state, if any. The equivalence hinges on our observation that for abstract machines, fusing a small-step specification yields a big-step specification. We illustrate this observation here with a recognizer for Dyck words, the CEK machine, and Krivine's machine with call/cc. The need for such a simple proof is motivated by our current work on small-step abstract machines as obtained by refocusing a function implementing a reduction semantics (a syntactic correspondence), and big-step abstract machines as obtained by CPS-transforming and then defunctionalizing a function implementing a big-step semantics (a functional correspondence)
On Termination for Faulty Channel Machines
A channel machine consists of a finite controller together with several fifo
channels; the controller can read messages from the head of a channel and write
messages to the tail of a channel. In this paper, we focus on channel machines
with insertion errors, i.e., machines in whose channels messages can
spontaneously appear. Such devices have been previously introduced in the study
of Metric Temporal Logic. We consider the termination problem: are all the
computations of a given insertion channel machine finite? We show that this
problem has non-elementary, yet primitive recursive complexity
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
Universality and programmability of quantum computers
Manin, Feynman, and Deutsch have viewed quantum computing as a kind of
universal physical simulation procedure. Much of the writing about quantum
logic circuits and quantum Turing machines has shown how these machines can
simulate an arbitrary unitary transformation on a finite number of qubits. The
problem of universality has been addressed most famously in a paper by Deutsch,
and later by Bernstein and Vazirani as well as Kitaev and Solovay. The quantum
logic circuit model, developed by Feynman and Deutsch, has been more prominent
in the research literature than Deutsch's quantum Turing machines. Quantum
Turing machines form a class closely related to deterministic and probabilistic
Turing machines and one might hope to find a universal machine in this class. A
universal machine is the basis of a notion of programmability. The extent to
which universality has in fact been established by the pioneers in the field is
examined and this key notion in theoretical computer science is scrutinised in
quantum computing by distinguishing various connotations and concomitant
results and problems.Comment: 17 pages, expands on arXiv:0705.3077v1 [quant-ph
Reactive Turing Machines
We propose reactive Turing machines (RTMs), extending classical Turing
machines with a process-theoretical notion of interaction, and use it to define
a notion of executable transition system. We show that every computable
transition system with a bounded branching degree is simulated modulo
divergence-preserving branching bisimilarity by an RTM, and that every
effective transition system is simulated modulo the variant of branching
bisimilarity that does not require divergence preservation. We conclude from
these results that the parallel composition of (communicating) RTMs can be
simulated by a single RTM. We prove that there exist universal RTMs modulo
branching bisimilarity, but these essentially employ divergence to be able to
simulate an RTM of arbitrary branching degree. We also prove that modulo
divergence-preserving branching bisimilarity there are RTMs that are universal
up to their own branching degree. Finally, we establish a correspondence
between executability and finite definability in a simple process calculus
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