Related papers: On Learning Polynomial Recursive Programs
Following some previous studies on restarting automata, we introduce a refined model - the h-lexicalized restarting automaton (h-RLWW). We argue that this model is useful for expressing lexicalized syntax in computational linguistics. We…
The well-known Nerode equivalence for finite words plays a fundamental role in our understanding of the class of regular languages. The equivalence leads to the Myhill-Nerode theorem and a canonical automaton, which in turn, is the basis of…
This paper introduces a new derivative parsing algorithm for recognition of parsing expression grammars. Derivative parsing is shown to have a polynomial worst-case time bound, an improvement on the exponential bound of the recursive…
Linear dependent types allow to precisely capture both the extensional behaviour and the time complexity of lambda terms, when the latter are evaluated by Krivine's abstract machine. In this work, we show that the same paradigm can be…
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…
The goal of this paper is to provide exact and terminating algorithms for the formal analysis of deterministic continuous-time control systems with affine input and polynomial state dynamics (in short, polynomial systems). We consider the…
Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…
Using recent developments in coalgebraic and monad-based semantics, we present a uniform study of various notions of machines, e.g. finite state machines, multi-stack machines, Turing machines, valence automata, and weighted automata. They…
Affine automata provide a finite-state computational model that preserves the linear-algebraic structure of quantum computation while operating entirely over the reals. Recent work has shown that affine automata can far surpass classical…
We present an algorithm to build an automaton from a rational expression. This approach introduces support for extended weighted expressions. Inspired by derived-term based algorithms, its core relies on a different construct, rational…
The value 1 problem is a decision problem for probabilistic automata over finite words: given a probabilistic automaton A, are there words accepted by A with probability arbitrarily close to 1? This problem was proved undecidable recently.…
Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks.…
We present a discrete-time formulation for the autonomous learning conjecture. The main feature of this formulation is the possibility to apply the autonomous learning scheme to systems in which the errors with respect to target functions…
In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which…
In this paper, we unravel a fundamental connection between weighted finite automata~(WFAs) and second-order recurrent neural networks~(2-RNNs): in the case of sequences of discrete symbols, WFAs and 2-RNNs with linear activation functions…
Partially ordered automata are automata where the transition relation induces a partial order on states. The expressive power of partially ordered automata is closely related to the expressivity of fragments of first-order logic on finite…
Recurrent neural networks are widely used in speech and language processing. Due to dependency on the past, standard algorithms for training these models, such as back-propagation through time (BPTT), cannot be efficiently parallelised.…
The identification of a deterministic finite automaton (DFA) from labeled examples is a well-studied problem in the literature; however, prior work focuses on the identification of monolithic DFAs. Although monolithic DFAs provide accurate…
We consider the value 1 problem for probabilistic automata over finite words: it asks whether a given probabilistic automaton accepts words with probability arbitrarily close to 1. This problem is known to be undecidable. However, different…
Watson-Crick automata are finite automata working on double strands. Extensive research work has already been done on non-deterministic Watson-Crick automata and on deterministic Watson-Crick automata. In this paper, we introduce a new…