4,584 research outputs found
An expressive completeness theorem for coalgebraic modal mu-calculi
Generalizing standard monadic second-order logic for Kripke models, we
introduce monadic second-order logic interpreted over coalgebras for an
arbitrary set functor. We then consider invariance under behavioral equivalence
of MSO-formulas. More specifically, we investigate whether the coalgebraic
mu-calculus is the bisimulation-invariant fragment of the monadic second-order
language for a given functor. Using automatatheoretic techniques and building
on recent results by the third author, we show that in order to provide such a
characterization result it suffices to find what we call an adequate uniform
construction for the coalgebraic type functor. As direct applications of this
result we obtain a partly new proof of the Janin-Walukiewicz Theorem for the
modal mu-calculus, avoiding the use of syntactic normal forms, and bisimulation
invariance results for the bag functor (graded modal logic) and all exponential
polynomial functors (including the "game functor"). As a more involved
application, involving additional non-trivial ideas, we also derive a
characterization theorem for the monotone modal mu-calculus, with respect to a
natural monadic second-order language for monotone neighborhood models.Comment: arXiv admin note: substantial text overlap with arXiv:1501.0721
Comparator automata in quantitative verification
The notion of comparison between system runs is fundamental in formal
verification. This concept is implicitly present in the verification of
qualitative systems, and is more pronounced in the verification of quantitative
systems. In this work, we identify a novel mode of comparison in quantitative
systems: the online comparison of the aggregate values of two sequences of
quantitative weights. This notion is embodied by {\em comparator automata}
({\em comparators}, in short), a new class of automata that read two infinite
sequences of weights synchronously and relate their aggregate values.
We show that {aggregate functions} that can be represented with B\"uchi
automaton result in comparators that are finite-state and accept by the B\"uchi
condition as well. Such {\em -regular comparators} further lead to
generic algorithms for a number of well-studied problems, including the
quantitative inclusion and winning strategies in quantitative graph games with
incomplete information, as well as related non-decision problems, such as
obtaining a finite representation of all counterexamples in the quantitative
inclusion problem.
We study comparators for two aggregate functions: discounted-sum and
limit-average. We prove that the discounted-sum comparator is -regular
iff the discount-factor is an integer. Not every aggregate function, however,
has an -regular comparator. Specifically, we show that the language of
sequence-pairs for which limit-average aggregates exist is neither
-regular nor -context-free. Given this result, we introduce the
notion of {\em prefix-average} as a relaxation of limit-average aggregation,
and show that it admits -context-free comparators
Alternating register automata on finite words and trees
We study alternating register automata on data words and data trees in
relation to logics. A data word (resp. data tree) is a word (resp. tree) whose
every position carries a label from a finite alphabet and a data value from an
infinite domain. We investigate one-way automata with alternating control over
data words or trees, with one register for storing data and comparing them for
equality. This is a continuation of the study started by Demri, Lazic and
Jurdzinski. From the standpoint of register automata models, this work aims at
two objectives: (1) simplifying the existent decidability proofs for the
emptiness problem for alternating register automata; and (2) exhibiting
decidable extensions for these models. From the logical perspective, we show
that (a) in the case of data words, satisfiability of LTL with one register and
quantification over data values is decidable; and (b) the satisfiability
problem for the so-called forward fragment of XPath on XML documents is
decidable, even in the presence of DTDs and even of key constraints. The
decidability is obtained through a reduction to the automata model introduced.
This fragment contains the child, descendant, next-sibling and
following-sibling axes, as well as data equality and inequality tests
Pushing undecidability of the isolation problem for probabilistic automata
This short note aims at proving that the isolation problem is undecidable for
probabilistic automata with only one probabilistic transition. This problem is
known to be undecidable for general probabilistic automata, without restriction
on the number of probabilistic transitions. In this note, we develop a
simulation technique that allows to simulate any probabilistic automaton with
one having only one probabilistic transition
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