Related papers: On the transition reduction problem for finite aut…
We follow language theoretic approach to synchronizing automata and \v{C}ern\'{y}'s conjecture initiated in a series of recent papers. We find a precise lower bound for the reset complexity of a principal ideal languages. Also we show a…
A non-deterministic call-by-need lambda-calculus \calc with case, constructors, letrec and a (non-deterministic) erratic choice, based on rewriting rules is investigated. A standard reduction is defined as a variant of left-most outermost…
Weighted automata over the nonnegative reals form a fundamental model for quantitative languages. We show that, up to scaling, this model collapses to probabilistic automata. Concretely, we prove that every weighted automaton whose…
In the constrained synchronization problem we ask if a given automaton admits a synchronizing word coming from a fixed regular constraint language. We show that intersecting a given constraint language with an ideal language decreases the…
We investigate the computational power of affine automata (AfAs) introduced in [4]. In particular, we present a simpler proof for how to change the cutpoint for any affine language and a method how to reduce error in bounded error case.…
A special class of symmetry reductions called nonclassical equivalence transformations is discussed in connection to a class of parameter identification problems represented by partial differential equations. These symmetry reductions…
Deterministic and nondeterministic finite automata with translucent letters were introduced by Nagy and Otto more than a decade ago as Cooperative Distributed systems of a kind of stateless restarting automata with window size one. These…
In 1978 Sakoda and Sipser raised the question of the cost, in terms of size of representations, of the transformation of two-way and one-way nondeterministic automata into equivalent two-way deterministic automata. Despite all the attempts,…
We introduce an affine generalization of counter automata, and analyze their ability as well as affine finite automata. Our contributions are as follows. We show that there is a language that can be recognized by exact realtime affine…
In the classic problem of sequence prediction, a predictor receives a sequence of values from an emitter and tries to guess the next value before it appears. The predictor masters the emitter if there is a point after which all of the…
This paper is devoted to finite state automata, regular expression matching, pattern recognition, and the exponential blow-up problem, which is the growing complexity of automata exponentially depending on regular expression length. This…
We propose to study value automata with filters, a natural generalization of regular cost automata to nondeterminism. Models such as weighted automata and Parikh automata appear naturally as specializations. Results on the expressiveness of…
The aim of this paper is to design the polynomial construction of a finite recognizer for hairpin completions of regular languages. This is achieved by considering completions as new expression operators and by applying derivation…
We explore two solutions to the problem of mistranslating rare words in neural machine translation. First, we argue that the standard output layer, which computes the inner product of a vector representing the context with all possible…
We study a categorical generalisation of tree automata, as $\Sigma$-algebras for a fixed endofunctor $\Sigma$ endowed with initial and final states. Under mild assumptions about the base category, we present a general minimisation algorithm…
End-to-end speech summarization (E2E SSum) directly summarizes input speech into easy-to-read short sentences with a single model. This approach is promising because it, in contrast to the conventional cascade approach, can utilize full…
The automatic complexity of a finite word (string) is an analogue for finite automata of Sipser's distinguishing complexity (1983) and was introduced by Shallit and Wang (2001). For a finite alphabet $\Sigma$ of at least two elements, we…
Automata over infinite words, also known as omega-automata, play a key role in the verification and synthesis of reactive systems. The spectrum of omega-automata is defined by two characteristics: the acceptance condition (e.g. B\"uchi or…
Unambiguous non-deterministic finite automata have intermediate expressive power and succinctness between deterministic and non-deterministic automata. It has been conjectured that every unambiguous non-deterministic one-way finite…
We consider the implementation of the transduction of automatic sequences, and their generalizations, in the Walnut software for solving decision problems in combinatorics on words. We provide a number of applications, including (a)…