60 research outputs found
Coalgebraic semantics of heavy-weighted automata
We study heavy-weighted automata, a generalization of weighted automata in which the
weights of the transitions can be any formal power series. We define their semantics in three
equivalent ways, and give some examples of how they can provide a more compact representation
of certain power series than ordinary weighted automata
Coalgebraic semantics of heavy-weighted automata
We study heavy-weighted automata, a generalization of weighted automata in which the
weights of the transitions can be any formal power series. We define their semantics in three
equivalent ways, and give some examples of how they can provide a more compact representation
of certain power series than ordinary weighted automata
Coalgebraic semantics of heavy-weighted automata
We study heavy-weighted automata, a generalization of weighted automata in which the
weights of the transitions can be any formal power series. We define their semantics in three
equivalent ways, and give some examples of how they can provide a more compact representation
of certain power series than ordinary weighted automata
Coalgebraic semantics of heavy-weighted automata
We study heavy-weighted automata, a generalization of weighted automata in which the
weights of the transitions can be any formal power series. We define their semantics in three
equivalent ways, and give some examples of how they can provide a more compact representation
of certain power series than ordinary weighted automata
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
Coalgebra for the working software engineer
Often referred to as ‘the mathematics of dynamical, state-based systems’, Coalgebra claims to provide a compositional and uniform framework to spec ify, analyse and reason about state and behaviour in computing. This paper addresses this claim by discussing why Coalgebra matters for the design of models and logics for computational phenomena. To a great extent, in this domain one is interested in properties that are preserved along the system’s evolution, the so-called ‘business rules’ or system’s invariants, as well as in liveness requirements, stating that e.g. some desirable outcome will be eventually produced. Both classes are examples of modal assertions, i.e. properties that are to be interpreted across a transition system capturing the system’s dynamics. The relevance of modal reasoning in computing is witnessed by the fact that most university syllabi in the area include some incursion into modal logic, in particular in its temporal variants. The novelty is that, as it happens with the notions of transition, behaviour, or observational equivalence, modalities in Coalgebra acquire a shape . That is, they become parametric on whatever type of behaviour, and corresponding coinduction scheme, seems appropriate for addressing the problem at hand. In this context, the paper revisits Coalgebra from a computational perspective, focussing on three topics central to software design: how systems are modelled, how models are composed, and finally, how properties of their behaviours can be expressed and verified.Fuzziness, as a way to express imprecision, or uncertainty, in computation is an important feature in a number of current application scenarios: from hybrid systems interfacing with sensor networks with error boundaries, to knowledge bases collecting data from often non-coincident human experts. Their abstraction in e.g. fuzzy transition systems led to a number of mathematical structures to model this sort of systems and reason about them. This paper adds two more elements to this family: two modal logics, framed as institutions, to reason about fuzzy transition systems and the corresponding processes. This paves the way to the development, in the second part of the paper, of an associated theory of structured specification for fuzzy computational systems
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 applied to several phenomena in automata theory, starting with determinization and
minimization (previously studied from a coalgebraic and duality theoretic perspective). We apply in particular these techniques to
Choffrut\u27s minimization algorithm for subsequential transducers and revisit Brzozowski\u27s minimization algorithm
Explicit Hopcroft's Trick in Categorical Partition Refinement
Algorithms for partition refinement are actively studied for a variety of
systems, often with the optimisation called Hopcroft's trick. However, the
low-level description of those algorithms in the literature often obscures the
essence of Hopcroft's trick. Our contribution is twofold. Firstly, we present a
novel formulation of Hopcroft's trick in terms of general trees with weights.
This clean and explicit formulation -- we call it Hopcroft's inequality -- is
crucially used in our second contribution, namely a general partition
refinement algorithm that is \emph{functor-generic} (i.e. it works for a
variety of systems such as (non-)deterministic automata and Markov chains).
Here we build on recent works on coalgebraic partition refinement but depart
from them with the use of fibrations. In particular, our fibrational notion of
-partitioning exposes a concrete tree structure to which Hopcroft's
inequality readily applies. It is notable that our fibrational framework
accommodates such algorithmic analysis on the categorical level of abstraction
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