348 research outputs found
Weighted first-order logics over semirings
We consider a first-order logic, a linear temporal logic, star-free expressions and counter-free Büchi automata, with weights, over idempotent, zerodivisor free and totally commutative complete semirings. We show the expressive
equivalence (of fragments) of these concepts, generalizing in the quantitative setup, the corresponding folklore result of formal language theory
Weighted Automata and Logics for Infinite Nested Words
Nested words introduced by Alur and Madhusudan are used to capture structures
with both linear and hierarchical order, e.g. XML documents, without losing
valuable closure properties. Furthermore, Alur and Madhusudan introduced
automata and equivalent logics for both finite and infinite nested words, thus
extending B\"uchi's theorem to nested words. Recently, average and discounted
computations of weights in quantitative systems found much interest. Here, we
will introduce and investigate weighted automata models and weighted MSO logics
for infinite nested words. As weight structures we consider valuation monoids
which incorporate average and discounted computations of weights as well as the
classical semirings. We show that under suitable assumptions, two resp. three
fragments of our weighted logics can be transformed into each other. Moreover,
we show that the logic fragments have the same expressive power as weighted
nested word automata.Comment: LATA 2014, 12 page
Architectures in parametric component-based systems: Qualitative and quantitative modelling
One of the key aspects in component-based design is specifying the software
architecture that characterizes the topology and the permissible interactions
of the components of a system. To achieve well-founded design there is need to
address both the qualitative and non-functional aspects of architectures. In
this paper we study the qualitative and quantitative formal modelling of
architectures applied on parametric component-based systems, that consist of an
unknown number of instances of each component. Specifically, we introduce an
extended propositional interaction logic and investigate its first-order level
which serves as a formal language for the interactions of parametric systems.
Our logics achieve to encode the execution order of interactions, which is a
main feature in several important architectures, as well as to model recursive
interactions. Moreover, we prove the decidability of equivalence,
satisfiability, and validity of first-order extended interaction logic
formulas, and provide several examples of formulas describing well-known
architectures. We show the robustness of our theory by effectively extending
our results for parametric weighted architectures. For this, we study the
weighted counterparts of our logics over a commutative semiring, and we apply
them for modelling the quantitative aspects of concrete architectures. Finally,
we prove that the equivalence problem of weighted first-order extended
interaction logic formulas is decidable in a large class of semirings, namely
the class (of subsemirings) of skew fields.Comment: 53 pages, 11 figure
Weighted Logics for Nested Words and Algebraic Formal Power Series
Nested words, a model for recursive programs proposed by Alur and Madhusudan,
have recently gained much interest. In this paper we introduce quantitative
extensions and study nested word series which assign to nested words elements
of a semiring. We show that regular nested word series coincide with series
definable in weighted logics as introduced by Droste and Gastin. For this we
establish a connection between nested words and the free bisemigroup. Applying
our result, we obtain characterizations of algebraic formal power series in
terms of weighted logics. This generalizes results of Lautemann, Schwentick and
Therien on context-free languages
Weighted Automata and Monadic Second Order Logic
Let S be a commutative semiring. M. Droste and P. Gastin have introduced in
2005 weighted monadic second order logic WMSOL with weights in S. They use a
syntactic fragment RMSOL of WMSOL to characterize word functions (power series)
recognizable by weighted automata, where the semantics of quantifiers is used
both as arithmetical operations and, in the boolean case, as quantification.
Already in 2001, B. Courcelle, J.Makowsky and U. Rotics have introduced a
formalism for graph parameters definable in Monadic Second order Logic, here
called MSOLEVAL with values in a ring R. Their framework can be easily adapted
to semirings S. This formalism clearly separates the logical part from the
arithmetical part and also applies to word functions.
In this paper we give two proofs that RMSOL and MSOLEVAL with values in S
have the same expressive power over words. One proof shows directly that
MSOLEVAL captures the functions recognizable by weighted automata. The other
proof shows how to translate the formalisms from one into the other.Comment: In Proceedings GandALF 2013, arXiv:1307.416
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