12,967 research outputs found
Root-Weighted Tree Automata and their Applications to Tree Kernels
In this paper, we define a new kind of weighted tree automata where the
weights are only supported by final states. We show that these automata are
sequentializable and we study their closures under classical regular and
algebraic operations. We then use these automata to compute the subtree kernel
of two finite tree languages in an efficient way. Finally, we present some
perspectives involving the root-weighted tree automata
Finite Model Finding for Parameterized Verification
In this paper we investigate to which extent a very simple and natural
"reachability as deducibility" approach, originated in the research in formal
methods in security, is applicable to the automated verification of large
classes of infinite state and parameterized systems. The approach is based on
modeling the reachability between (parameterized) states as deducibility
between suitable encodings of states by formulas of first-order predicate
logic. The verification of a safety property is reduced to a pure logical
problem of finding a countermodel for a first-order formula. The later task is
delegated then to the generic automated finite model building procedures. In
this paper we first establish the relative completeness of the finite
countermodel finding method (FCM) for a class of parameterized linear arrays of
finite automata. The method is shown to be at least as powerful as known
methods based on monotonic abstraction and symbolic backward reachability.
Further, we extend the relative completeness of the approach and show that it
can solve all safety verification problems which can be solved by the
traditional regular model checking.Comment: 17 pages, slightly different version of the paper is submitted to
TACAS 201
An Efficient Normalisation Procedure for Linear Temporal Logic and Very Weak Alternating Automata
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 , where
and 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.Comment: This is the extended version of the referenced conference paper and
contains an appendix with additional materia
Minimisation of Multiplicity Tree Automata
We consider the problem of minimising the number of states in a multiplicity
tree automaton over the field of rational numbers. We give a minimisation
algorithm that runs in polynomial time assuming unit-cost arithmetic. We also
show that a polynomial bound in the standard Turing model would require a
breakthrough in the complexity of polynomial identity testing by proving that
the latter problem is logspace equivalent to the decision version of
minimisation. The developed techniques also improve the state of the art in
multiplicity word automata: we give an NC algorithm for minimising multiplicity
word automata. Finally, we consider the minimal consistency problem: does there
exist an automaton with states that is consistent with a given finite
sample of weight-labelled words or trees? We show that this decision problem is
complete for the existential theory of the rationals, both for words and for
trees of a fixed alphabet rank.Comment: Paper to be published in Logical Methods in Computer Science. Minor
editing changes from previous versio
LTL Parameter Synthesis of Parametric Timed Automata
The parameter synthesis problem for parametric timed automata is undecidable
in general even for very simple reachability properties. In this paper we
introduce restrictions on parameter valuations under which the parameter
synthesis problem is decidable for LTL properties. The investigated bounded
integer parameter synthesis problem could be solved using an explicit
enumeration of all possible parameter valuations. We propose an alternative
symbolic zone-based method for this problem which results in a faster
computation. Our technique extends the ideas of the automata-based approach to
LTL model checking of timed automata. To justify the usefulness of our
approach, we provide experimental evaluation and compare our method with
explicit enumeration technique.Comment: 23 pages, extended versio
Evaluating Datalog via Tree Automata and Cycluits
We investigate parameterizations of both database instances and queries that
make query evaluation fixed-parameter tractable in combined complexity. We show
that clique-frontier-guarded Datalog with stratified negation (CFG-Datalog)
enjoys bilinear-time evaluation on structures of bounded treewidth for programs
of bounded rule size. Such programs capture in particular conjunctive queries
with simplicial decompositions of bounded width, guarded negation fragment
queries of bounded CQ-rank, or two-way regular path queries. Our result is
shown by translating to alternating two-way automata, whose semantics is
defined via cyclic provenance circuits (cycluits) that can be tractably
evaluated.Comment: 56 pages, 63 references. Journal version of "Combined Tractability of
Query Evaluation via Tree Automata and Cycluits (Extended Version)" at
arXiv:1612.04203. Up to the stylesheet, page/environment numbering, and
possible minor publisher-induced changes, this is the exact content of the
journal paper that will appear in Theory of Computing Systems. Update wrt
version 1: latest reviewer feedbac
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