Nested Weighted Automata

Chatterjee, Krishnendu; Henzinger, Thomas A.; Otop, Jan

doi:10.1109/lics.2015.72

Cited by 10 publications

(2 citation statements)

References 11 publications

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“…Weighted automata have found applications in speech and language processing [16], and they have been extended for modeling systems and verifying quantitative properties of these systems [17]. The studied models for the latter purpose include Nested Weighted Automata [18], a two-level variant of weighted automata for infinite strings. The computational problems that are relevant for quantitative verification are analysis questions such as universality and equivalence.…”

Section: Related Workmentioning

confidence: 99%

Streamable regular transductions

Alur

Fisman

Mamouras

et al. 2020

Theoretical Computer Science

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Motivated by real-time monitoring and data processing applications, we develop a formal theory of quantitative queries for streaming data that can be evaluated efficiently. We consider the model of unambiguous Cost Register Automata (CRAs), which are machines that combine finite-state control (for identifying regular patterns) with a finite set of data registers (for computing numerical aggregates). The definition of CRAs is parameterized by the collection of numerical operations that can be applied to the registers. These machines give rise to the class of streamable regular transductions (SR), and to the class of streamable linear regular transductions (SLR) when the register updates are copyless, i.e. every register appears at most once the right-handside expressions of the updates. We give a logical characterization of the class SR (resp., SLR) using MSO-definable transformations from strings to DAGs (resp., trees) without backward edges. Additionally, we establish that the two classes SR and SLR are closed under operations that are relevant for designing query languages. Finally, we study the relationship with weighted automata (WA), and show that CRAs over a suitably chosen set of operations correspond to WA, thus establishing that WA are a special case of CRAs.

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Section: Related Workmentioning

confidence: 99%

Streamable regular transductions

Alur

Fisman

Mamouras

et al. 2020

Theoretical Computer Science

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“…However, instead of rejecting the implementation, one can quantify the distance between a measured trace and the specification. Among all implementations that violate a specification, the closer the implementation traces are to the specification, the better [6,8,13]. The edit distance problem is also the basis for repairing specifications [2,3].The TED problem answers a fine-grained question with a fixed bound on the number of edit operations.…”

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confidence: 99%

Edit Distance for Pushdown Automata

Chatterjee

Henzinger

Ibsen-Jensen

et al. 2015

Automata, Languages, and Programming

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Abstract. The edit distance between two words w1, w2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w1 to w2. The edit distance generalizes to languages L1, L2, where the edit distance from L1 to L2 is the minimal number k such that for every word from L1 there exists a word in L2 with edit distance at most k. We study the edit distance computation problem between pushdown automata and their subclasses. The problem of computing edit distance to a pushdown automaton is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for the following problems: (1) deciding whether, for a given threshold k, the edit distance from a pushdown automaton to a finite automaton is at most k, and (2) deciding whether the edit distance from a pushdown automaton to a finite automaton is finite.

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Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs

Chatterjee

Ibsen-Jensen

Pavlogiannis

2015

Computer Aided Verification

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We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff property, the ratio property, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let n denote the number of nodes of a graph, m the number of edges (for constant treewidth graphs m = O(n)) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a multiplicative factor of in time O(n · log(n/ )) and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time O(n · log(|a · b|)) = O(n · log(n · W )), when the output is a b , as compared to the previously best known algorithm with running time O(n 2 · log(n · W )). Third, for the minimum initial credit problem we show that (i) for general graphs the problem can be solved in O(n 2 · m) time and the associated decision problem can be solved in O(n · m) time, improving the previous known O(n 3 · m · log(n · W )) and O(n 2 · m) bounds, respectively; and (ii) for constant treewidth graphs we present an algorithm that requires O(n · log n) time, improving the previous known O(n 4 · log(n · W )) bound. We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.

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Nested Weighted Automata

Cited by 10 publications

References 11 publications

Streamable regular transductions

Streamable regular transductions

Edit Distance for Pushdown Automata

Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs

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