Related papers: Automatic functions, linear time and learning

Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent…

Automata learning is a technique that has successfully been applied in verification, with the automaton type varying depending on the application domain. Adaptations of automata learning algorithms for increasingly complex types of automata…

Sequential learning, also called lifelong learning, studies the problem of learning tasks in a sequence with access restricted to only the data of the current task. In this paper we look at a scenario with fixed model capacity, and…

This paper summarizes the fundamental expressiveness, closure, and decidability properties of various finite-state automata classes with multiple input tapes. It also includes an original algorithm for the intersection of one-way…

Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…

We prove the equivalence of two classes of counter machines and one class of distributed automata. Our counter machines operate on finite words, which they read from left to right while incrementing or decrementing a fixed number of…

Finite (word) state transducers extend finite state automata by defining a binary relation over finite words, called rational relation. If the rational relation is the graph of a function, this function is said to be rational. The class of…

Methods proposed in the literature towards continual deep learning typically operate in a task-based sequential learning setup. A sequence of tasks is learned, one at a time, with all data of current task available but not of previous or…

Challenging the standard notion of totality in computable functions, one has that, given any sufficiently expressive formal axiomatic system, there are total functions that, although computable and "intuitively" understood as being total,…

Active learning of finite automata has been vigorously pursued for the purposes of analysis and explanation of black-box systems. In this paper, we study an L*-style learning algorithm for weighted automata over the max-plus semiring. The…

In neural networks literature, there is a strong interest in identifying and defining activation functions which can improve neural network performance. In recent years there has been a renovated interest of the scientific community in…

Linear temporal logic was introduced in order to reason about reactive systems. It is often considered with respect to infinite words, to specify the behaviour of long-running systems. One can consider more general models for linear time,…

Modern learning systems increasingly interact with data that evolve over time and depend on hidden internal state. We ask a basic question: when is such a dynamical system learnable from observations alone? This paper proposes a research…

We consider the arithmetic complexity of index sets of uniformly computably enumerable families learnable under different learning criteria. We determine the exact complexity of these sets for the standard notions of finite learning,…

Activation functions (AF) are necessary components of neural networks that allow approximation of functions, but AFs in current use are usually simple monotonically increasing functions. In this paper, we propose trainable compound AF (TCA)…

Rule 110 is a cellular automaton that performs repeated simultaneous updates of an infinite row of binary values. The values are updated in the following way: 0s are changed to 1s at all positions where the value to the right is a 1, while…

In a jumping finite automaton, the input head can jump to an arbitrary position within the remaining input after reading and consuming a symbol. We characterize the corresponding class of languages in terms of special shuffle expressions…

Tasks with complex temporal structures and long horizons pose a challenge for reinforcement learning agents due to the difficulty in specifying the tasks in terms of reward functions as well as large variances in the learning signals. We…

We study learning of indexed families from positive data where a learner can freely choose a hypothesis space (with uniformly decidable membership) comprising at least the languages to be learned. This abstracts a very universal learning…

Transformers trained on huge text corpora exhibit a remarkable set of capabilities, e.g., performing basic arithmetic. Given the inherent compositional nature of language, one can expect the model to learn to compose these capabilities,…