Abstract We introduce and investigate tree-walking-storage automata, which are finite-state devices equipped with a tree-like storage. The automata are generalized stack automata, where the linear stack storage is replaced by a non-linear tree-like stack. Therefore, tree-walking-storage automata have the ability to explore the interior of the tree storage without altering the contents, where the possible moves of the tree pointer correspond to those of tree-walking automata. In addition, a tree-walking-storage automaton can append (push) non-existent descendants to a tree node and remove (pop) leaves from the tree. As for classical stack automata, we also consider non-erasing and checking variants. As a first step to investigate these models we consider the computational capacities of deterministic one-way variants. In particular, a primary focus lies on comparing the different variants of tree-walking-storage automata as well as with classical stack automata, enabling us to draw a complete picture. Basic closure properties of the induced families of languages are shown. In particular, we consider Boolean operations and several AFL operations.

Abstract We study deterministic tree-walking-storage automata, which are finite-state devices equipped with a tree-like storage. These automata are generalized stack automata, where the linear stack storage is replaced by a non-linear tree-like stack. Therefore, tree-walking-storage automata have the ability to explore the interior of the tree storage without altering the contents, with the possible moves of the tree pointer corresponding to those of tree-walking automata. In addition, a tree-walking-storage automaton can append (push) non-existent descendants to a tree node and remove (pop) leaves from the tree. Here we are particularly considering the capacities of deterministic tree-walking-storage automata working in real time. It is shown that even the non-erasing variant can accept rather complicated unary languages as, for example, the language of words whose lengths are powers of two, or the language of words whose lengths are double Fibonacci numbers. Comparing the computational capacities with automata from the classical automata hierarchy, we derive that the family of languages accepted by real-time deterministic (non-erasing) tree-walking-storage automata is located between the regular and the deterministic context-sensitive languages. Moreover, the families are incomparable with the families of context-free and growing context-sensitive languages. It turns out that the devices under consideration accept unary languages in non-erasing mode that cannot be accepted by any classical stack automaton, even in erasing mode and arbitrary time. Basic closure properties of the induced families of languages are shown. In particular, we consider Boolean operations and AFL operations. It turns out that the two families in question have the same properties and, in particular, share all but one of these closure properties with the important family of deterministic context-free languages. Then, we consider the computational capacity of the counterpart to counter- and stack-counter automata, where the set of stack symbols is a singleton. Finally, we explore several decidability problems and show, that even for devices with a single tree symbol, the problems are all non-semidecidable by reductions of non-semidecidable problems of Turing machines.

Article Free Access Share on Techniques for partial evaluation of imperative languages Author: Uwe Meyer AG Informatik/FB Mathematik, Justus-Liebig-Universität Giessen, Arndtstr. 2, W-6300 Giessen, Germany AG Informatik/FB Mathematik, Justus-Liebig-Universität Giessen, Arndtstr. 2, W-6300 Giessen, GermanyView Profile Authors Info & Claims PEPM '91: Proceedings of the 1991 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulationMay 1991 Pages 94–105https://doi.org/10.1145/115865.115876Published:01 May 1991Publication History 29citation318DownloadsMetricsTotal Citations29Total Downloads318Last 12 Months34Last 6 weeks2 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

A formal approach to deal with several types of grids in the context of multigrid algorithms is presented. The approach serves as a framework for describing the definition and manipulation of grids as well as the specification of typical grid algorithms. Furthermore, it is useful to define the transformation of high-level grid algorithms into parallel programs. The proposed method is used within the Suspense specification and transformation system to handle simple and staggered logically rectangular grids.