6,714 research outputs found
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
A Logic for Non-Deterministic Parallel Abstract State Machines
We develop a logic which enables reasoning about single steps of
non-deterministic parallel Abstract State Machines (ASMs). Our logic builds
upon the unifying logic introduced by Nanchen and St\"ark for reasoning about
hierarchical (parallel) ASMs. Our main contribution to this regard is the
handling of non-determinism (both bounded and unbounded) within the logical
formalism. Moreover, we do this without sacrificing the completeness of the
logic for statements about single steps of non-deterministic parallel ASMs,
such as invariants of rules, consistency conditions for rules, or step-by-step
equivalence of rules.Comment: arXiv admin note: substantial text overlap with arXiv:1602.0748
The dome: An unexpectedly simple failure of determinism
Newton's equations of motion tell us that a mass at rest at the apex of a dome with the shape specified here can spontaneously move. It has been suggested that this indeterminism should be discounted since it draws on an incomplete rendering of Newtonian physics, or it is "unphysical," or it employs illicit idealizations. I analyze and reject each of these reasons. Copyright 2008 by the Philosophy of Science Association. All rights reserved
Forward Analysis and Model Checking for Trace Bounded WSTS
We investigate a subclass of well-structured transition systems (WSTS), the
bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete
deterministic ones, which we claim provide an adequate basis for the study of
forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth.
Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered
previously for the termination of forward analysis, boundedness is decidable.
Boundedness turns out to be a valuable restriction for WSTS verification, as we
show that it further allows to decide all -regular properties on the
set of infinite traces of the system
Exploring the Boundaries of Monad Tensorability on Set
We study a composition operation on monads, equivalently presented as large
equational theories. Specifically, we discuss the existence of tensors, which
are combinations of theories that impose mutual commutation of the operations
from the component theories. As such, they extend the sum of two theories,
which is just their unrestrained combination. Tensors of theories arise in
several contexts; in particular, in the semantics of programming languages, the
monad transformer for global state is given by a tensor. We present two main
results: we show that the tensor of two monads need not in general exist by
presenting two counterexamples, one of them involving finite powerset (i.e. the
theory of join semilattices); this solves a somewhat long-standing open
problem, and contrasts with recent results that had ruled out previously
expected counterexamples. On the other hand, we show that tensors with bounded
powerset monads do exist from countable powerset upwards
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