3,730 research outputs found
A Relational Derivation of a Functional Program
This article is an introduction to the use of relational calculi in deriving programs. Using the relational caluclus Ruby, we derive a functional program that adds one bit to a binary number to give a new binary number. The resulting program is unsurprising, being the standard quot;, but the derivation illustrates a number of points about working with relations rather than with functions
How sufficient conditions are related for topology-preserving reductions
A crucial issue in digital topology is to ensure topology preservation for reductions acting on binary pictures (i.e., operators that never change a white point to black one). Some sufficient conditions for topology-preserving reductions have been proposed for pictures on the three possible regular partitionings of the plane (i.e., the triangular, the square, and the hexagonal grids). In this paper, the relationships among these conditions are stated
The three dimensions of proofs
In this document, we study a 3-polygraphic translation for the proofs of SKS,
a formal system for classical propositional logic. We prove that the free
3-category generated by this 3-polygraph describes the proofs of classical
propositional logic modulo structural bureaucracy. We give a 3-dimensional
generalization of Penrose diagrams and use it to provide several pictures of a
proof. We sketch how local transformations of proofs yield a non contrived
example of 4-dimensional rewriting.Comment: 38 pages, 50 figure
Stability and Complexity of Minimising Probabilistic Automata
We consider the state-minimisation problem for weighted and probabilistic
automata. We provide a numerically stable polynomial-time minimisation
algorithm for weighted automata, with guaranteed bounds on the numerical error
when run with floating-point arithmetic. Our algorithm can also be used for
"lossy" minimisation with bounded error. We show an application in image
compression. In the second part of the paper we study the complexity of the
minimisation problem for probabilistic automata. We prove that the problem is
NP-hard and in PSPACE, improving a recent EXPTIME-result.Comment: This is the full version of an ICALP'14 pape
A Relational Derivation of a Functional Program
This article is an introduction to the use of relational calculi in deriving programs. Using the relational caluclus Ruby, we derive a functional program that adds one bit to a binary number to give a new binary number. The resulting program is unsurprising, being the standard quot;, but the derivation illustrates a number of points about working with relations rather than with functions
Parallel dynamics and computational complexity of the Bak-Sneppen model
The parallel computational complexity of the Bak-Sneppen evolution model is
studied. It is shown that Bak-Sneppen histories can be generated by a massively
parallel computer in a time that is polylogarithmic in the length of the
history. In this parallel dynamics, histories are built up via a nested
hierarchy of avalanches. Stated in another way, the main result is that the
logical depth of producing a Bak-Sneppen history is exponentially less than the
length of the history. This finding is surprising because the self-organized
critical state of the Bak-Sneppen model has long range correlations in time and
space that appear to imply that the dynamics is sequential and history
dependent. The parallel dynamics for generating Bak-Sneppen histories is
contrasted to standard Bak-Sneppen dynamics. Standard dynamics and an alternate
method for generating histories, conditional dynamics, are both shown to be
related to P-complete natural decision problems implying that they cannot be
efficiently implemented in parallel.Comment: 37 pages, 12 figure
The Geometry of Concurrent Interaction: Handling Multiple Ports by Way of Multiple Tokens (Long Version)
We introduce a geometry of interaction model for Mazza's multiport
interaction combinators, a graph-theoretic formalism which is able to
faithfully capture concurrent computation as embodied by process algebras like
the -calculus. The introduced model is based on token machines in which
not one but multiple tokens are allowed to traverse the underlying net at the
same time. We prove soundness and adequacy of the introduced model. The former
is proved as a simulation result between the token machines one obtains along
any reduction sequence. The latter is obtained by a fine analysis of
convergence, both in nets and in token machines
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