Input-Driven Tissue P Automata

We introduce several variants of input-driven tissue P automata where the rules to be applied only depend on the input symbol. Both strings and multisets are considered as input objects; the strings are either read from an input tape or defined by the sequence of symbols taken in, and the multisets are given in an input cell at the beginning of a computation, enclosed in a vesicle. Additional symbols generated during a computation are stored in this vesicle, too. An input is accepted when the vesicle reaches a final cell and it is empty. The computational power of some variants of input-driven tissue P automata is illustrated by examples and compared with the power of the input-driven variants of other automata as register machines and counter automata

Deterministic Real-Time Tree-Walking-Storage Automata

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 Fibonacci numbers. Comparing the computational capacities with automata from the classical automata hierarchy, we derive that the families of languages accepted by real-time deterministic (non-erasing) tree-walking-storage automata is located between the regular and the deterministic context-sensitive languages. There is a context-free language that is not accepted by any real-time deterministic tree-walking-storage automaton. On the other hand, these devices accept a unary language 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 (complementation, union, intersection) and AFL operations (union, intersection with regular languages, homomorphism, inverse homomorphism, concatenation, iteration). 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.Comment: In Proceedings NCMA 2023, arXiv:2309.0733

Beyond operator-precedence grammars and languages

Operator Precedence Languages (OPL) are deterministic context-free and have desirable properties. OPL are parallely parsable, and, when structurally compatible, are closed under Boolean operations, concatenation and star; they include the Input Driven languages. OPL use three relations between two terminal symbols, to assign syntax structure to words. We extend such relations to k-tuples of consecutive symbols, in agreement with strictly locally testable regular languages. For each k, the new corresponding class of Higher-order Operator Precedence languages properly includes the OPL and enjoy many of their properties. OPL are a strict hierarchy based on k, which contains maximal languages

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers