Weighted Tree Automata over Valuation Monoids and Their Characterization by Weighted Logics

Weighted automata model quantitative aspects of systems like memory or power consumption. Recently, Chatterjee, Doyen, and Henzinger introduced a new kind of weighted automata which compute objectives like the average cost or the long-time peak power consumption. In these automata, operations like average, limit superior, limit inferior, limit average, or discounting are used to assign values to finite or infinite words. In general, these weighted automata are not semiring weighted anymore. Here, we establish a connection between such new kinds of weighted automata and weighted logics. We show that suitable weighted MSO logics and these new weighted automata are expressively equivalent, both for finite and infinite words. The constructions employed are effective, leading to decidability results for the weighted logic formulas considered.

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“…Moreover, results similar to the ones of this paper were also obtained for finite traces [26] and finite trees [11].…”

Section: Resultssupporting

confidence: 79%

Weighted automata and weighted MSO logics for average and long-time behaviors

Droste

Meinecke

2012

Information and Computation

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101

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“…In [12], a more general cost model was investigated, where the weight of a run may be determined by a global valuation function. It was shown that for bi-locally finite bimonoids, W T A capture the expressive power of several semantics of full W M SO L. In [13], weighted finite transition systems with weights from naturally ordered semirings were considered.…”

Section: Introductionmentioning

confidence: 99%

Effective optimization with weighted automata on decomposable trees

2014

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In this paper, we consider quantitative optimization problems on decomposable discrete systems. We restrict ourselves to labeled trees as the description of the systems and we use weighted automata on them as our computational model. We introduce a new kind of labeled decomposable trees, sum-like weighted labeled trees, and propose a method, which allows us to reduce the solution of an optimization problem, defined in a fragment of Weighted Monadic Second Order Logic, on such a tree to the solution of effectively derived problems, defined in the same logic, on its components with some additional post-processing. The approach originates from a method, proposed first by Feferman and Vaught in 1959, which we adapt and generalize. We adapt the method to the case of (fragments of) Weighted Monadic Second Order Logic and generalize it to the case of sum-like labeled trees rather than disjoint union and product. The main result of the paper may be applied in the wide range of optimization problems, such as critical path analysis or project planning, network optimization, generalized assignment problem, routing and scheduling as well as in the modern document languages like XML, image processing and compression, probabilistic systems or speech-to-text processing.

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“…The logic may be used in order to describe data mining problems, decision making, planning and scheduling. Additionally, in [9], a strong relationship between W T A over ptv-monoids and the fragments of the W M SOL was established. Let Σ be a ranked alphabet and (D, +, V al, 0) a tv-monoid.…”

Section: C2 Expressive Power Of Weighted Monadic Second Order Logicmentioning

confidence: 99%

“…However, the larger the particular fragment gets, the more restrictions on the underlying ptv-monoid we need. The main theorem of [9] states (cf. the exact definitions in the paper):…”

Section: C2 Expressive Power Of Weighted Monadic Second Order Logicmentioning

confidence: 99%

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A Uniform Approach to Incremental Automated Reasoning on Strongly Distributed Structures

Ravve¹,

Volkovich²,

Weber³

EPiC Series in Computing

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We introduce the notion of strongly distributed structures and present a uniform approach to incremental automated reasoning on them. The approach is based on a systematic use of two logical reduction techniques: Feferman-Vaught reductions and syntactically defined translation schemes. The distributed systems are presented as logical structures A's. We propose a uniform template for methods, which allow for a certain cost evaluation of formulae of logic L over A from values of formulae over its components and values of formulae over the index structure I. Given logic L, structure A as a composition of structures Ai, i ∈ I, index structure I and formula φ of the logic to be evaluated on A, the question is: what is the reduction sequence for φ if any. We show that if we may prove preservation theorems for L as well as if A is a strongly distributed composition of its components then the corresponding reduction sequence for A may be effectively computed. We show that the approach works for many extensions of F OL but not for all. The considered extensions of F OL are suitable candidates for modeling languages for components and services, used in incremental automated reasoning, data mining, decision making, planning and scheduling. A short complexity analysis of the method is also provided.

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Weighted Tree Automata over Valuation Monoids and Their Characterization by Weighted Logics

Cited by 27 publications

References 40 publications

Weighted automata and weighted MSO logics for average and long-time behaviors

Weighted automata and weighted MSO logics for average and long-time behaviors

Effective optimization with weighted automata on decomposable trees

A Uniform Approach to Incremental Automated Reasoning on Strongly Distributed Structures

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