Related papers: On Learning Polynomial Recursive Programs
A central question in the theory of automata is which classes of automata can be minimized in polynomial time. We close the remaining gaps for deterministic and history-deterministic automata over infinite words by proving that…
Reversible weighted automata are introduced and considered in a specific setting where the weights are taken from a nontrivial locally finite commutative ring such as a finite field. It is shown that the supports of series realised by such…
We present an algorithm for extraction of a probabilistic deterministic finite automaton (PDFA) from a given black-box language model, such as a recurrent neural network (RNN). The algorithm is a variant of the exact-learning algorithm L*,…
The RPNI algorithm (Oncina, Garcia 1992) constructs deterministic finite automata from finite sets of negative and positive example words. We propose and analyze an extension of this algorithm to deterministic $\omega$-automata with…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata…
We present a novel algorithm that uses exact learning and abstraction to extract a deterministic finite automaton describing the state dynamics of a given trained RNN. We do this using Angluin's L* algorithm as a learner and the trained RNN…
We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences. These sequences arise naturally in the study of nonlinear extensions of weighted automata, where…
This work studies the question of learning probabilistic deterministic automata from language models. For this purpose, it focuses on analyzing the relations defined on algebraic structures over strings by equivalences and similarities on…
We study the learnability of symbolic finite state automata (SFA), a model shown useful in many applications in software verification. The state-of-the-art literature on this topic follows the query learning paradigm, and so far all…
We present a formal and constructive theory showing that probabilistic finite automata (PFAs) can be exactly simulated using symbolic feedforward neural networks. Our architecture represents state distributions as vectors and transitions as…
Nondeterministic weighted automata are finite automata with numerical weights on transitions. They define quantitative languages L that assign to each word w a real number L(w). The value of an infinite word w is computed as the maximal…
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…
Automata learning is a popular technique used to automatically construct an automaton model from queries. Much research went into devising ad hoc adaptations of algorithms for different types of automata. The CALF project seeks to unify…
Weighted finite automata (WFA) can expressively model functions defined over strings but are inherently linear models. Given the recent successes of nonlinear models in machine learning, it is natural to wonder whether ex-tending WFA to the…
Finite-state automata are a very effective tool in natural language processing. However, in a variety of applications and especially in speech precessing, it is necessary to consider more general machines in which arcs are assigned weights…
We study the computational power of real-time finite automata that have been augmented with a vector of dimension k, and programmed to multiply this vector at each step by an appropriately selected $k \times k$ matrix. Only one entry of the…
We propose a new automaton model, called quantified data automata over words, that can model quantified invariants over linear data structures, and build poly-time active learning algorithms for them, where the learner is allowed to query…
In this work, we study the fully automated inference of expected result values of probabilistic programs in the presence of natural programming constructs such as procedures, local variables and recursion. While crucial, capturing these…
We derive the P-finite recurrences for classes of sequences with ordinary generating function containing roots of polynomials. The focus is on establishing the D-finite differential equations such that the familiar steps of reducing their…