Coalgebra Learning via Duality

Automata learning is a popular technique for inferring minimal automata through membership and equivalence queries. In this paper, we generalise learning to the theory of coalgebras. The approach relies on the use of logical formulas as tests, based on a dual adjunction between states and logical theories. This allows us to learn, e.g., labelled transition systems, using Hennessy-Milner logic. Our main contribution is an abstract learning algorithm, together with a proof of correctness and termination

Learning Quantum Finite Automata with Queries

{\it Learning finite automata} (termed as {\it model learning}) has become an important field in machine learning and has been useful realistic applications. Quantum finite automata (QFA) are simple models of quantum computers with finite memory. Due to their simplicity, QFA have well physical realizability, but one-way QFA still have essential advantages over classical finite automata with regard to state complexity (two-way QFA are more powerful than classical finite automata in computation ability as well). As a different problem in {\it quantum learning theory} and {\it quantum machine learning}, in this paper, our purpose is to initiate the study of {\it learning QFA with queries} (naturally it may be termed as {\it quantum model learning}), and the main results are regarding learning two basic one-way QFA: (1) We propose a learning algorithm for measure-once one-way QFA (MO-1QFA) with query complexity of polynomial time; (2) We propose a learning algorithm for measure-many one-way QFA (MM-1QFA) with query complexity of polynomial-time, as well.Comment: 18pages; comments are welcom

Residual Nominal Automata

Nominal automata are models for accepting languages over infinite alphabets. In this paper we refine the hierarchy of nondeterministic nominal automata, by developing the theory of residual nominal automata. In particular, we show that they admit canonical minimal representatives, and that the universality problem becomes decidable. We also study exact learning of these automata, and settle questions that were left open about their learnability via observations

Canonical automata via distributive law homomorphisms

The classical powerset construction is a standard method converting a nondeterministic automaton into a deterministic one recognising the same language. Recently, the powerset construction has been lifted to a more general framework that converts an automaton with side-effects, given by a monad, into a deterministic automaton accepting the same language. The resulting automaton has additional algebraic properties, both in the state space and transition structure, inherited from the monad. In this paper, we study the reverse construction and present a framework in which a deterministic automaton with additional algebraic structure over a given monad can be converted into an equivalent succinct automaton with side-effects. Apart from recovering examples from the literature, such as the canonical residual finite-state automaton and the \'atomaton, we discover a new canonical automaton for a regular language by relating the free vector space monad over the two element field to the neighbourhood monad. Finally, we show that every regular language satisfying a suitable property parametric in two monads admits a size-minimal succinct acceptor

Optimizing Automata Learning via Monads

Automata learning has been successfully applied in the verification of hardware and software. The size of the automaton model learned is a bottleneck for scalability, and hence optimizations that enable learning of compact representations are important. This paper exploits monads, both as a mathematical structure and a programming construct, to design, prove correct, and implement a wide class of such optimizations. The former perspective on monads allows us to develop a new algorithm and accompanying correctness proofs, building upon a general framework for automata learning based on category theory. The new algorithm is parametric on a monad, which provides a rich algebraic structure to capture non-determinism and other side-effects. We show that our approach allows us to uniformly capture existing algorithms, develop new ones, and add optimizations. The latter perspective allows us to effortlessly translate the theory into practice: we provide a Haskell library implementing our general framework, and we show experimental results for two specific instances: non-deterministic and weighted automata

To Heck With Ethics: Thinking About Public Issues With a Framework for CS Students

This paper proposes that the ethics class in the CS curriculum incorporate the Lawrence Lessig model of regulation as an analytical tool for social issues. Lessig’s use of the notion of architecture, the rules and boundaries of the sometimes artificial world within which social issues play out, is particularly resonant with computing professionals. The CS curriculum guidelines include only ethical frameworks as the tool for our students to engage with societal issues. The regulation framework shows how the market, law, social norms, and architecture can all be applied toward understanding social issues