2,344 research outputs found
Synthesis of Data Word Transducers
In reactive synthesis, the goal is to automatically generate an
implementation from a specification of the reactive and non-terminating
input/output behaviours of a system. Specifications are usually modelled as
logical formulae or automata over infinite sequences of signals
(-words), while implementations are represented as transducers. In the
classical setting, the set of signals is assumed to be finite. In this paper,
we consider data -words instead, i.e., words over an infinite alphabet.
In this context, we study specifications and implementations respectively given
as automata and transducers extended with a finite set of registers. We
consider different instances, depending on whether the specification is
nondeterministic, universal or deterministic, and depending on whether the
number of registers of the implementation is given or not.
In the unbounded setting, we show undecidability for both universal and
nondeterministic specifications, while decidability is recovered in the
deterministic case. In the bounded setting, undecidability still holds for
nondeterministic specifications, but can be recovered by disallowing tests over
input data. The generic technique we use to show the latter result allows us to
reprove some known result, namely decidability of bounded synthesis for
universal specifications
Synthesis of Data Word Transducers
In reactive synthesis, the goal is to automatically generate an implementation from a specification of the reactive and non-terminating input/output behaviours of a system. Specifications are usually modelled as logical formulae or automata over infinite sequences of signals (omega-words), while implementations are represented as transducers. In the classical setting, the set of signals is assumed to be finite. In this paper, we consider data omega-words instead, i.e., words over an infinite alphabet. In this context, we study specifications and implementations respectively given as automata and transducers extended with a finite set of registers. We consider different instances, depending on whether the specification is nondeterministic, universal or deterministic, and depending on whether the number of registers of the implementation is given or not.
In the unbounded setting, we show undecidability for both universal and non-deterministic specifications, while decidability is recovered in the deterministic case. In the bounded setting, undecidability still holds for non-deterministic specifications, but can be recovered by disallowing tests over input data. The generic technique we use to show the latter result allows us to reprove some known result, namely decidability of bounded synthesis for universal specifications
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
In the Maze of Data Languages
In data languages the positions of strings and trees carry a label from a
finite alphabet and a data value from an infinite alphabet. Extensions of
automata and logics over finite alphabets have been defined to recognize data
languages, both in the string and tree cases. In this paper we describe and
compare the complexity and expressiveness of such models to understand which
ones are better candidates as regular models
Automata Minimization: a Functorial Approach
In this paper we regard languages and their acceptors - such as deterministic
or weighted automata, transducers, or monoids - as functors from input
categories that specify the type of the languages and of the machines to
categories that specify the type of outputs. Our results are as follows:
A) We provide sufficient conditions on the output category so that
minimization of the corresponding automata is guaranteed.
B) We show how to lift adjunctions between the categories for output values
to adjunctions between categories of automata.
C) We show how this framework can be instantiated to unify several phenomena
in automata theory, starting with determinization, minimization and syntactic
algebras. We provide explanations of Choffrut's minimization algorithm for
subsequential transducers and of Brzozowski's minimization algorithm in this
setting.Comment: journal version of the CALCO 2017 paper arXiv:1711.0306
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