104,627 research outputs found
ASMs and Operational Algorithmic Completeness of Lambda Calculus
We show that lambda calculus is a computation model which can step by step
simulate any sequential deterministic algorithm for any computable function
over integers or words or any datatype. More formally, given an algorithm above
a family of computable functions (taken as primitive tools, i.e., kind of
oracle functions for the algorithm), for every constant K big enough, each
computation step of the algorithm can be simulated by exactly K successive
reductions in a natural extension of lambda calculus with constants for
functions in the above considered family. The proof is based on a fixed point
technique in lambda calculus and on Gurevich sequential Thesis which allows to
identify sequential deterministic algorithms with Abstract State Machines. This
extends to algorithms for partial computable functions in such a way that
finite computations ending with exceptions are associated to finite reductions
leading to terms with a particular very simple feature.Comment: 37 page
Deterministic regular functions of infinite words
Regular functions of infinite words are (partial) functions realized by
deterministic two-way transducers with infinite look-ahead. Equivalently, Alur
et. al. have shown that they correspond to functions realized by deterministic
Muller streaming string transducers, and to functions defined by
MSO-transductions. Regular functions are however not computable in general (for
a classical extension of Turing computability to infinite inputs), and we
consider in this paper the class of deterministic regular functions of infinite
words, realized by deterministic two-way transducers without look-ahead. We
prove that it is a well-behaved class of functions: they are computable, closed
under composition, characterized by the guarded fragment of MSO-transductions,
by deterministic B\"uchi streaming string transducers, by deterministic two-way
transducers with finite look-ahead, and by finite compositions of sequential
functions and one fixed basic function called map-copy-reverse.Comment: 45 page
Intensional and Extensional Semantics of Bounded and Unbounded Nondeterminism
We give extensional and intensional characterizations of nondeterministic
functional programs: as structure preserving functions between biorders, and as
nondeterministic sequential algorithms on ordered concrete data structures
which compute them. A fundamental result establishes that the extensional and
intensional representations of non-deterministic programs are equivalent, by
showing how to construct a unique sequential algorithm which computes a given
monotone and stable function, and describing the conditions on sequential
algorithms which correspond to continuity with respect to each order.
We illustrate by defining may and must-testing denotational semantics for a
sequential functional language with bounded and unbounded choice operators. We
prove that these are computationally adequate, despite the non-continuity of
the must-testing semantics of unbounded nondeterminism. In the bounded case, we
prove that our continuous models are fully abstract with respect to may and
must-testing by identifying a simple universal type, which may also form the
basis for models of the untyped lambda-calculus. In the unbounded case we
observe that our model contains computable functions which are not denoted by
terms, by identifying a further "weak continuity" property of the definable
elements, and use this to establish that it is not fully abstract
On optimal quantization rules for some problems in sequential decentralized detection
We consider the design of systems for sequential decentralized detection, a
problem that entails several interdependent choices: the choice of a stopping
rule (specifying the sample size), a global decision function (a choice between
two competing hypotheses), and a set of quantization rules (the local decisions
on the basis of which the global decision is made). This paper addresses an
open problem of whether in the Bayesian formulation of sequential decentralized
detection, optimal local decision functions can be found within the class of
stationary rules. We develop an asymptotic approximation to the optimal cost of
stationary quantization rules and exploit this approximation to show that
stationary quantizers are not optimal in a broad class of settings. We also
consider the class of blockwise stationary quantizers, and show that
asymptotically optimal quantizers are likelihood-based threshold rules.Comment: Published as IEEE Transactions on Information Theory, Vol. 54(7),
3285-3295, 200
Degree of Sequentiality of Weighted Automata
Weighted automata (WA) are an important formalism to describe quantitative properties. Obtaining equivalent deterministic machines is a longstanding research problem. In this paper we consider WA with a set semantics, meaning that the semantics is given by the set of weights of accepting runs. We focus on multi-sequential WA that are defined as finite unions of sequential WA. The problem we address is to minimize the size of this union. We call this minimum the degree of sequentiality of (the relation realized by) the WA.
For a given positive integer k, we provide multiple characterizations of relations realized by a union of k sequential WA over an infinitary finitely generated group: a Lipschitz-like machine independent property, a pattern on the automaton (a new twinning property) and a subclass of cost register automata. When possible, we effectively translate a WA into an equivalent union of k sequential WA. We also provide a decision procedure for our twinning property for commutative computable groups thus allowing to compute the degree of sequentiality. Last, we show that these results also hold for word transducers and that the associated decision problem is PSPACE
-complete
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