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Register a new userAlternating Automata on Data Trees and XPath Satisfiability
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Added by
Ranko Lazic
Publication date
2010
fields
Informatics Engineering
and research's language is
English
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A data tree is an unranked ordered tree whose every node is labelled by a letter from a finite alphabet and an element (datum) from an infinite set, where the latter can only be compared for equality. The article considers alternating automata on data trees that can move downward and rightward, and have one register for storing data. The main results are that nonemptiness over finite data trees is decidable but not primitive recursive, and that nonemptiness of safety automata is decidable but not elementary. The proofs use nondeterministic tree automata with faulty counters. Allowing upward moves, leftward moves, or two registers, each causes undecidability. As corollaries, decidability is obtained for two data-sensitive fragments of the XPath query language.
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A data word is a sequence of pairs of a letter from a finite alphabet and an element from an infinite set, where the latter can only be compared for equality. Safety one-way alternating automata with one register on infinite data words are considered, their nonemptiness is shown EXPSPACE-complete, and their inclusion decidable but not primitive recursive. The same complexity bounds are obtained for satisfiability and refinement, respectively, for the safety fragment of linear temporal logic with freeze quantification. Dropping the safety restriction, adding past temporal operators, or adding one more register, each causes undecidability.
In the mid 80s, Lichtenstein, Pnueli, and Zuck proved a classical theorem stating that every formula of Past LTL (the extension of LTL with past operators) is equivalent to a formula of the form $bigwedge_{i=1}^n mathbf{G}mathbf{F} varphi_i vee mathbf{F}mathbf{G} psi_i$, where $varphi_i$ and $psi_i$ contain only past operators. Some years later, Chang, Manna, and Pnueli built on this result to derive a similar normal form for LTL. Both normalisation procedures have a non-elementary worst-case blow-up, and follow an involved path from formulas to counter-free automata to star-free regular expressions and back to formulas. We improve on both points. We present a direct and purely syntactic normalisation procedure for LTL yielding a normal form, comparable to the one by Chang, Manna, and Pnueli, that has only a single exponential blow-up. As an application, we derive a simple algorithm to translate LTL into deterministic Rabin automata. The algorithm normalises the formula, translates it into a special very weak alternating automaton, and applies a simple determinisation procedure, valid only for these special automata.
Delivering effective data analytics is of crucial importance to the interpretation of the multitude of biological datasets currently generated by an ever increasing number of high throughput techniques. Logic programming has much to offer in this area. Here, we detail advances that highlight two of the strengths of logical formalisms in developing data analytic solutions in biological settings: access to large relational databases and building analytical pipelines collecting graph information from multiple sources. We present significant advances on the bio_db package which serves biological databases as Prolog facts that can be served either by in-memory loading or via database backends. These advances include modularising the underlying architecture and the incorporation of datasets from a second organism (mouse). In addition, we introduce a number of data analytics tools that operate on these datasets and are bundled in the analysis package: bio_analytics. Emphasis in both packages is on ease of installation and use. We highlight the general architecture of our components based approach. An experimental graphical user interface via SWISH for local installation is also available. Finally, we advocate that biological data analytics is a fertile area which can drive further innovation in applied logic programming.
Controller synthesis for general linear temporal logic (LTL) objectives is a challenging task. The standard approach involves translating the LTL objective into a deterministic parity automaton (DPA) by means of the Safra-Piterman construction. One of the challenges is the size of the DPA, which often grows very fast in practice, and can reach double exponential size in the length of the LTL formula. In this paper we describe a single exponential translation from limit-deterministic Buchi automata (LDBA) to DPA, and show that it can be concatenated with a recent efficient translation from LTL to LDBA to yield a double exponential, enquote{Safraless} LTL-to-DPA construction. We also report on an implementation, a comparison with the SPOT library, and performance on several sets of formulas, including instances from the 2016 SyntComp competition.
One can think of some physical evolutions as being the emergent-effective result of a microscopic discrete model. Inspired by classical coarse-graining procedures, we provide a simple procedure to coarse-grain color-blind quantum cellular automata that follow Goldilocks rules. The procedure consists in (i) space-time grouping the quantum cellular automaton (QCA) in cells of size $N$; (ii) projecting the states of a cell onto its borders, connecting them with the fine dynamics; (iii) describing the overall dynamics by the border states, that we call signals; and (iv) constructing the coarse-grained dynamics for different sizes $N$ of the cells. A byproduct of this simple toy-model is a general discrete analog of the Stokes law. Moreover we prove that in the spacetime limit, the automaton converges to a Dirac free Hamiltonian. The QCA we introduce here can be implemented by present-day quantum platforms, such as Rydberg arrays, trapped ions, and superconducting qbits. We hope our study can pave the way to a richer understanding of those systems with limited resolution.
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