8 research outputs found
Higher-Order Operator Precedence Languages
Floyd's Operator Precedence (OP) languages are a deterministic context-free
family having many desirable properties. They are locally and parallely
parsable, and languages having a compatible structure are closed under Boolean
operations, concatenation and star; they properly include the family of Visibly
Pushdown (or Input Driven) languages. OP languages are based on three relations
between any two consecutive terminal symbols, which assign syntax structure to
words. We extend such relations to k-tuples of consecutive terminal symbols, by
using the model of strictly locally testable regular languages of order k at
least 3. The new corresponding class of Higher-order Operator Precedence
languages (HOP) properly includes the OP languages, and it is still included in
the deterministic (also in reverse) context free family. We prove Boolean
closure for each subfamily of structurally compatible HOP languages. In each
subfamily, the top language is called max-language. We show that such languages
are defined by a simple cancellation rule and we prove several properties, in
particular that max-languages make an infinite hierarchy ordered by parameter
k. HOP languages are a candidate for replacing OP languages in the various
applications where they have have been successful though sometimes too
restrictive.Comment: In Proceedings AFL 2017, arXiv:1708.0622
Toward a theory of input-driven locally parsable languages
If a context-free language enjoys the local parsability property then, no matter how the source string is segmented, each segment can be parsed independently, and an efficient parallel parsing algorithm becomes possible. The new class of locally chain parsable languages (LCPLs), included in the deterministic context-free language family, is here defined by means of the chain-driven automaton and characterized by decidable properties of grammar derivations. Such automaton decides whether to reduce or not a substring in a way purely driven by the terminal characters, thus extending the well-known concept of input-driven (ID) alias visibly pushdown machines. The LCPL family extends and improves the practically relevant Floyd's operator-precedence (OP) languages which are known to strictly include the ID languages, and for which a parallel-parser generator exists
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
Digging input-driven pushdown automata
Input-driven pushdown automata (IDPDA) are pushdown automata where the next action on the pushdown store (push, pop, nothing) is solely governed by the input symbol. Nowadays such devices are usually defined such that popping from the empty pushdown does not block the computation but continues it with empty pushdown. Here, we consider IDPDAs that have a more balanced behavior concerning pushing and popping. Digging input-driven pushdown automata (DIDPDA) are basically IDPDAs that, when forced to pop from the empty pushdown, dig a hole of the shape of the popped symbol in the bottom of the pushdown. Popping further symbols from a pushdown having a hole at the bottom deepens the current hole furthermore. The hole can only be filled up by pushing symbols previously popped. We study the impact of the new behavior of DIDPDAs on their power and compare their capacities with the capacities of ordinary IDPDAs and tinput-driven pushdown automata which are basically IDPDAs whose input may be preprocessed by length-preserving finite state transducers. It turns out that the capabilities are incomparable. We address the determinization of DIDPDAs and their descriptional complexity, closure properties, and decidability questions