19,601 research outputs found
Practical State Machines for Computer Software and Engineering
This paper introduces methods for describing properties of possibly very
large state machines in terms of solutions to recursive functions and applies
those methods to computer systems
Some undecidability results for asynchronous transducers and the Brin-Thompson group 2V
Using a result of Kari and Ollinger, we prove that the torsion problem for
elements of the Brin-Thompson group 2V is undecidable. As a result, we show
that there does not exist an algorithm to determine whether an element of the
rational group R of Grigorchuk, Nekrashevich, and Sushchanskii has finite
order. A modification of the construction gives other undecidability results
about the dynamics of the action of elements of 2V on Cantor Space.
Arzhantseva, Lafont, and Minasyanin prove in 2012 that there exists a finitely
presented group with solvable word problem and unsolvable torsion problem. To
our knowledge, 2V furnishes the first concrete example of such a group, and
gives an example of a direct undecidability result in the extended family of R.
Thompson type groups.Comment: 16 pages, 3 figure
Regular Combinators for String Transformations
We focus on (partial) functions that map input strings to a monoid such as
the set of integers with addition and the set of output strings with
concatenation. The notion of regularity for such functions has been defined
using two-way finite-state transducers, (one-way) cost register automata, and
MSO-definable graph transformations. In this paper, we give an algebraic and
machine-independent characterization of this class analogous to the definition
of regular languages by regular expressions. When the monoid is commutative, we
prove that every regular function can be constructed from constant functions
using the combinators of choice, split sum, and iterated sum, that are analogs
of union, concatenation, and Kleene-*, respectively, but enforce unique (or
unambiguous) parsing. Our main result is for the general case of
non-commutative monoids, which is of particular interest for capturing regular
string-to-string transformations for document processing. We prove that the
following additional combinators suffice for constructing all regular
functions: (1) the left-additive versions of split sum and iterated sum, which
allow transformations such as string reversal; (2) sum of functions, which
allows transformations such as copying of strings; and (3) function
composition, or alternatively, a new concept of chained sum, which allows
output values from adjacent blocks to mix.Comment: This is the full version, with omitted proofs and constructions, of
the conference paper currently in submissio
A Genetic Programming Approach to Designing Convolutional Neural Network Architectures
The convolutional neural network (CNN), which is one of the deep learning
models, has seen much success in a variety of computer vision tasks. However,
designing CNN architectures still requires expert knowledge and a lot of trial
and error. In this paper, we attempt to automatically construct CNN
architectures for an image classification task based on Cartesian genetic
programming (CGP). In our method, we adopt highly functional modules, such as
convolutional blocks and tensor concatenation, as the node functions in CGP.
The CNN structure and connectivity represented by the CGP encoding method are
optimized to maximize the validation accuracy. To evaluate the proposed method,
we constructed a CNN architecture for the image classification task with the
CIFAR-10 dataset. The experimental result shows that the proposed method can be
used to automatically find the competitive CNN architecture compared with
state-of-the-art models.Comment: This is the revised version of the GECCO 2017 paper. The code of our
method is available at https://github.com/sg-nm/cgp-cn
Tight polynomial worst-case bounds for loop programs
In 2008, Ben-Amram, Jones and Kristiansen showed that for a simple programming language - representing non-deterministic imperative programs with bounded loops, and arithmetics limited to addition and multiplication - it is possible to decide precisely whether a program has certain growth-rate properties, in particular whether a computed value, or the program's running time, has a polynomial growth rate. A natural and intriguing problem was to move from answering the decision problem to giving a quantitative result, namely, a tight polynomial upper bound. This paper shows how to obtain asymptotically-tight, multivariate, disjunctive polynomial bounds for this class of programs. This is a complete solution: whenever a polynomial bound exists it will be found. A pleasant surprise is that the algorithm is quite simple; but it relies on some subtle reasoning. An important ingredient in the proof is the forest factorization theorem, a strong structural result on homomorphisms into a finite monoid
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