96 research outputs found
Recognizable tree series with discounting
We consider weighted tree automata with discounting over commutative semirings. For their behaviors we establish a Kleene theorem and an MSO-logic characterization. We introduce also weighted Muller tree automata with discounting over the max-plus and the min-plus semirings, and we show their expressive equivalence with two fragments of weighted MSO-sentences
Logics of Finite Hankel Rank
We discuss the Feferman-Vaught Theorem in the setting of abstract model
theory for finite structures. We look at sum-like and product-like binary
operations on finite structures and their Hankel matrices. We show the
connection between Hankel matrices and the Feferman-Vaught Theorem. The largest
logic known to satisfy a Feferman-Vaught Theorem for product-like operations is
CFOL, first order logic with modular counting quantifiers. For sum-like
operations it is CMSOL, the corresponding monadic second order logic. We
discuss whether there are maximal logics satisfying Feferman-Vaught Theorems
for finite structures.Comment: Appeared in YuriFest 2015, held in honor of Yuri Gurevich's 75th
birthday. The final publication is available at Springer via
http://dx.doi.org/10.1007/978-3-319-23534-9_1
Kleene theorems for skew formal power series
We investigate the theory of skew (formal) power series introduced by Droste, Kuske [5, 6], if the basic semiring is a Conway semiring. This yields Kleene Theorems for skew power series, whose supports contain finite and infinite words. We then develop a theory of convergence in semirings of skew power series based on the discrete convergence. As an application this yields a Kleene Theorem proved already by Droste, Kuske [5]
Weighted first-order logics over semirings
We consider a first-order logic, a linear temporal logic, star-free expressions and counter-free BĂĽchi 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
Contributions to multi-view modeling and the multi-view consistency problem for infinitary languages and discrete systems
The modeling of most large and complex systems, such as embedded, cyber-physical, or distributed systems, necessarily involves many designers. The multiple stakeholders carry their own perspectives of the system under development in order to meet a variety of objectives, and hence they derive their own models for the same system. This practice is known as multiview modeling, where the distinct models of a system are called views. Inevitably, the separate views are related, and possible overlaps may give rise to inconsistencies. Checking for multiview consistency is key to multi-view modeling approaches, especially when a global model for the system is absent, and can only be synthesized from the views.
The present thesis provides an overview of the representative related work in multi-view modeling, and contributes to the formal study of multi-view modeling and the multi-view consistency problem for views and systems described as sets of behaviors. In particular, two distinct settings are investigated, namely, infinitary languages, and discrete systems. In the former research, a system and its views are described by mixed automata, which accept both finite and infinite words, and the corresponding infinitary languages. The views are obtained from the system by projections of an alphabet of events (system domain) onto a subalphabet (view domain), while inverse projections are used in the other direction. A systematic study is provided for mixed automata, and their languages are proved to be closed under union, intersection, complementation, projection, and inverse projection. In the sequel, these results are used in order to solve the multi-view consistency problem in the infinitary language setting.
The second research introduces the notion of periodic sampling abstraction functions, and investigates the multi-view consistency problem for symbolic discrete systems with respect to these functions. Apart from periodic samplings, inverse periodic samplings are also introduced, and the closure of discrete systems under these operations is investigated. Then, three variations of the multi-view consistency problem are considered, and their relations are discussed. Moreover, an algorithm is provided for detecting view inconsistencies. The algorithm is sound but it may fail to detect all inconsistencies, as it relies on a state-based reachability, and inconsistencies may also involve the transition structure of the system
Approximation in Description Logics: How Weighted Tree Automata Can Help to Define the Required Concept Comparison Measures in FLâ‚€
Recently introduced approaches for relaxed query answering, approximately defining concepts, and approximately solving unification problems in Description Logics have in common that they are based on the use of concept comparison measures together with a threshold construction. In this paper, we will briefly review these approaches, and then show how weighted automata working on infinite trees can be used to construct computable concept comparison measures for FLâ‚€ that are equivalence invariant w.r.t. general TBoxes. This is a first step towards employing such measures in the mentioned approximation approaches.Accepted to LATA 201
Contramodules
Contramodules are module-like algebraic structures endowed with infinite
summation (or, occasionally, integration) operations satisfying natural axioms.
Introduced originally by Eilenberg and Moore in 1965 in the case of coalgebras
over commutative rings, contramodules experience a small renaissance now after
being all but forgotten for three decades between 1970-2000. Here we present a
review of various definitions and results related to contramodules (drawing
mostly from our monographs and preprints arXiv:0708.3398, arXiv:0905.2621,
arXiv:1202.2697, arXiv:1209.2995, arXiv:1512.08119, arXiv:1710.02230,
arXiv:1705.04960, arXiv:1808.00937) - including contramodules over corings,
topological associative rings, topological Lie algebras and topological groups,
semicontramodules over semialgebras, and a "contra version" of the
Bernstein-Gelfand-Gelfand category O. Several underived manifestations of the
comodule-contramodule correspondence phenomenon are discussed.Comment: LaTeX 2e with pb-diagram and xy-pic; 93 pages, 3 commutative
diagrams; v.4: updated to account for the development of the theory over the
four years since Spring 2015: introduction updated, references added, Remark
2.2 inserted, Section 3.3 rewritten, Sections 3.7-3.8 adde
A Definability Dichotomy for Finite Valued CSPs
Finite valued constraint satisfaction problems are a formalism for describing many natural optimisation problems, where constraints on the values that variables can take come with rational weights and the aim is to find an assignment of minimal cost. Thapper and Zivny have recently established a complexity dichotomy for valued constraint languages. They show that each such languages either gives rise to a polynomial-time solvable optimisation problem, or to an NP-hard one, and establish a criterion to distinguish the two cases. We refine the dichotomy by showing that all optimisation problems in the first class are definable in fixed-point language with counting, while all languages in the second class are not definable, even in infinitary logic with counting. Our definability dichotomy is not conditional on any complexity-theoretic assumption
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