相关论文: Linearly bounded infinite graphs
We introduce tree stack automata as a new class of automata with storage and identify a restricted form of tree stack automata that recognises exactly the multiple context-free languages.
Regular colored graphs are dual representations of pure colored D-dimensional complexes. These graphs can be classified with respect to an integer, their degree, much like maps are characterized by the genus. We analyse the structure of…
Context-free languages are widely used to describe the syntax of programming languages and natural languages. Usually, we describe a context-free language mathematically with the help of context-free grammar (for generation) or pushdown…
A $d$-limited automaton is a Turing machine that may rewrite each input cell at most~$d$ times. Hibbard (1967) showed that for every $d \geq 2$ such automata recognize all context-free languages and that deterministic $d$-limited automata…
Let $X=(V\!X,E\!X)$ be an infinite, locally finite, connected graph without loops or multiple edges. We consider the edges to be oriented, and $E\!X$ is equipped with an involution which inverts the orientation. Each oriented edge is…
Two new classes of finite automata, called General hexagonal Boustrophedon finite automata and General hexagonal returning finite automata operating on hexagonal grids, are introduced and analyzed. The work establishes the theoretical…
During the last decades, classical models in language theory have been extended by control mechanisms defined by monoids. We study which monoids cause the extensions of context-free grammars, finite automata, or finite state transducers to…
In many ways, graphs are the main modality of data we receive from nature. This is due to the fact that most of the patterns we see, both in natural and artificial systems, are elegantly representable using the language of graph structures.…
A robot's ability to understand or ground natural language instructions is fundamentally tied to its knowledge about the surrounding world. We present an approach to grounding natural language utterances in the context of factual…
In a recent paper, Altenbernd, Thomas and W\"ohrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the B\"uchi and Muller…
Automaton models are often seen as interpretable models. Interpretability itself is not well defined: it remains unclear what interpretability means without first explicitly specifying objectives or desired attributes. In this paper, we…
Tree-structured recursive neural networks (TreeRNNs) for sentence meaning have been successful for many applications, but it remains an open question whether the fixed-length representations that they learn can support tasks as demanding as…
We show that for any monoid M, the family of languages accepted by M-automata (or equivalently, generated by regular valence grammars over M) is completely determined by that part of M which lies outside the maximal ideal. Hence, every such…
We present a generalization of standard Turing machines based on allowing unusual tapes. We present a set of reasonable constraints on tape geometry and classify all tapes conforming to these constraints. Surprisingly, this generalization…
Symbolic automata are finite state automata that support potentially infinite alphabets, such as the set of rational numbers, generally applied to regular expressions/languages over finite words. In symbolic automata (or automata modulo…
In this work we study a non-linear generalization based on affine transformations of probabilistic and quantum automata proposed recently by D\'iaz-Caro and Yakary{\i}lmaz \cite{DCY16A} referred as affine automata. First, we present…
We investigate structural implications arising from the condition that a given directed graph does not interpret, in the sense of primitive positive interpretation with parameters or orbits, every finite structure. Our results generalize…
Graph games of infinite length are a natural model for open reactive processes: one player represents the controller, trying to ensure a given specification, and the other represents a hostile environment. The evolution of the system…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
Linear automata are automata with two reading heads starting from the two extremes of the input, are equivalent to 5' -> 3' Watson-Crick (WK) finite automata. The heads read the input in opposite directions and the computation finishes when…