The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful abstraction, algorithms for computing a finite automaton for the downward closure of a given language have been established only for few language classes. This wo...

Pushdown systems are a model of computation equipped with one stack where only the top of the stack is inspected and modified in each step of transitions. Although this is a natural restriction, some extensions of pushdown systems require more general operations on stack: conditional pushdown systems inspect the whole stack contents and discrete timed pushdown systems increment the ages of the ...

Shuffle projection is motivated by the verification of safety properties of special parameterized systems. Basic definitions and properties, especially related to alphabetic homomorphisms, are presented. The relation between iterated shuffle products and shuffle projections is shown. A special class of multi-counter automata is introduced, to formulate shuffle projection in terms of computation...

Mitogen-activated protein kinases (MAPKs) are involved in a variety of intracellular events such as gene expression, cell proliferation, and programmed cell death. MAPKs are activated by dual phosphorylation on threonine and tyrosine residues through sequential activation of protein kinases. Recent studies have shown that the protein kinases involved in MAPK signal transductions might be organi...

How should one apply deep learning to tasks such as morphological reinflection, which stochastically edit one string to get another? A recent approach to such sequence-to-sequence tasks is to compress the input string into a vector that is then used to generate the output string, using recurrent neural networks. In contrast, we propose to keep the traditional architecture, which uses a finite-s...

A text is a word together with an additional linear order on it. We study quantitative models for texts, i.e. text series which assign to texts elements of a semiring. We introduce an algebraic notion of recognizability following Reutenauer and Bozapalidis as well as weighted automata for texts combining an automaton model of Lodaya and Weil with a model of Ésik and Németh. After that we show t...

We introduce a logic, calledLT , to express proper-ties of transductions, i.e. binary relations from input to output(finite) words. InLT , the input/output dependencies are modeledvia an origin function which associates with any position of theoutput word, the input position from which it originates. The logicLT can express all MSO-definable functions, and is incompa...

Copyless streaming string transducers (copyless SST) have been introduced by R. Alur and P. Černý in 2010 as a one-way deterministic automata model to define transductions of finite strings. SST extend state with set variables which store intermediate output strings, those can be combined updated all along the run, linear manner, i.e., no variable content copied on transitions. It is known that...