6,695 research outputs found
On the Commutative Equivalence of Context-Free Languages
The problem of the commutative equivalence of context-free and regular languages is studied. In particular conditions ensuring that a context-free language of exponential growth is commutatively equivalent with a regular language are investigated
Coding-theorem Like Behaviour and Emergence of the Universal Distribution from Resource-bounded Algorithmic Probability
Previously referred to as `miraculous' in the scientific literature because
of its powerful properties and its wide application as optimal solution to the
problem of induction/inference, (approximations to) Algorithmic Probability
(AP) and the associated Universal Distribution are (or should be) of the
greatest importance in science. Here we investigate the emergence, the rates of
emergence and convergence, and the Coding-theorem like behaviour of AP in
Turing-subuniversal models of computation. We investigate empirical
distributions of computing models in the Chomsky hierarchy. We introduce
measures of algorithmic probability and algorithmic complexity based upon
resource-bounded computation, in contrast to previously thoroughly investigated
distributions produced from the output distribution of Turing machines. This
approach allows for numerical approximations to algorithmic
(Kolmogorov-Chaitin) complexity-based estimations at each of the levels of a
computational hierarchy. We demonstrate that all these estimations are
correlated in rank and that they converge both in rank and values as a function
of computational power, despite fundamental differences between computational
models. In the context of natural processes that operate below the Turing
universal level because of finite resources and physical degradation, the
investigation of natural biases stemming from algorithmic rules may shed light
on the distribution of outcomes. We show that up to 60\% of the
simplicity/complexity bias in distributions produced even by the weakest of the
computational models can be accounted for by Algorithmic Probability in its
approximation to the Universal Distribution.Comment: 27 pages main text, 39 pages including supplement. Online complexity
calculator: http://complexitycalculator.com
Automata Tutor v3
Computer science class enrollments have rapidly risen in the past decade.
With current class sizes, standard approaches to grading and providing
personalized feedback are no longer possible and new techniques become both
feasible and necessary. In this paper, we present the third version of Automata
Tutor, a tool for helping teachers and students in large courses on automata
and formal languages. The second version of Automata Tutor supported automatic
grading and feedback for finite-automata constructions and has already been
used by thousands of users in dozens of countries. This new version of Automata
Tutor supports automated grading and feedback generation for a greatly extended
variety of new problems, including problems that ask students to create regular
expressions, context-free grammars, pushdown automata and Turing machines
corresponding to a given description, and problems about converting between
equivalent models - e.g., from regular expressions to nondeterministic finite
automata. Moreover, for several problems, this new version also enables
teachers and students to automatically generate new problem instances. We also
present the results of a survey run on a class of 950 students, which shows
very positive results about the usability and usefulness of the tool
Probabilistic Constraint Logic Programming
This paper addresses two central problems for probabilistic processing
models: parameter estimation from incomplete data and efficient retrieval of
most probable analyses. These questions have been answered satisfactorily only
for probabilistic regular and context-free models. We address these problems
for a more expressive probabilistic constraint logic programming model. We
present a log-linear probability model for probabilistic constraint logic
programming. On top of this model we define an algorithm to estimate the
parameters and to select the properties of log-linear models from incomplete
data. This algorithm is an extension of the improved iterative scaling
algorithm of Della-Pietra, Della-Pietra, and Lafferty (1995). Our algorithm
applies to log-linear models in general and is accompanied with suitable
approximation methods when applied to large data spaces. Furthermore, we
present an approach for searching for most probable analyses of the
probabilistic constraint logic programming model. This method can be applied to
the ambiguity resolution problem in natural language processing applications.Comment: 35 pages, uses sfbart.cl
Efficient Generator of Mathematical Expressions for Symbolic Regression
We propose an approach to symbolic regression based on a novel variational
autoencoder for generating hierarchical structures, HVAE. It combines simple
atomic units with shared weights to recursively encode and decode the
individual nodes in the hierarchy. Encoding is performed bottom-up and decoding
top-down. We empirically show that HVAE can be trained efficiently with small
corpora of mathematical expressions and can accurately encode expressions into
a smooth low-dimensional latent space. The latter can be efficiently explored
with various optimization methods to address the task of symbolic regression.
Indeed, random search through the latent space of HVAE performs better than
random search through expressions generated by manually crafted probabilistic
grammars for mathematical expressions. Finally, EDHiE system for symbolic
regression, which applies an evolutionary algorithm to the latent space of
HVAE, reconstructs equations from a standard symbolic regression benchmark
better than a state-of-the-art system based on a similar combination of deep
learning and evolutionary algorithms.\v{z}Comment: 35 pages, 11 tables, 7 multi-part figures, Machine learning
(Springer) and journal track of ECML/PKDD 202
Compiler Design: Theory, Tools, and Examples
Compiler design is a subject which many believe to be fundamental and vital to computer science. It is a subject which has been studied intensively since the early 1950’s and continues to be an important research field today. Compiler design is an important part of the undergraduate curriculum for many reasons: (1) It provides students with a better understanding of and appreciation for programming languages. (2) The techniques used in compilers can be used in other applications with command languages. (3) It provides motivation for the study of theoretic topics. (4) It is a good vehicle for an extended programming project.
There are several compiler design textbooks available today, but most have been written for graduate students. Here at Rowan University, our students have had difficulty reading these books. However, I felt it was not the subject matter that was the problem, but the way it was presented. I was sure that if concepts were presented at a slower pace, with sample problems and diagrams to illustrate the concepts, that our students would be able to master the concepts. This is what I have attempted to do in writing this book.https://rdw.rowan.edu/oer/1001/thumbnail.jp
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