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Statistic Analysis for Probabilistic Processes
, 2010
"... We associate a statistical vector to a trace and a geometrical embedding to a Markov Decision Process, based on a distance on words, and study basic Membership and Equivalence problems. The Membership problem for a trace w and a Markov Decision Process S decides if there exists a strategy on S whi ..."
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We associate a statistical vector to a trace and a geometrical embedding to a Markov Decision Process, based on a distance on words, and study basic Membership and Equivalence problems. The Membership problem for a trace w and a Markov Decision Process S decides if there exists a strategy on S which generates with high probability traces close to w. We prove that Membership of a trace is testable and Equivalence of MDPs is polynomial time approximable. For Probabilistic Automata, Membership is not testable, and approximate Equivalence is undecidable. We give a class of properties, based on results concerning the structure of the tail σfield of a finite Markov chain,
Approximations in ModelChecking and Testing
, 2008
"... We describe different approximations in the context of ModelChecking and Testing. ..."
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We describe different approximations in the context of ModelChecking and Testing.
Software Testing with Active Learning in a
"... Abstract. Motivated by Structural Statistical Software Testing (SSST), this paper is interested in sampling the feasible execution paths in the control flow graph of the program being tested. For some complex programs, the fraction of feasible paths becomes tiny, ranging in [10 −10, 10 −5]. When rel ..."
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Abstract. Motivated by Structural Statistical Software Testing (SSST), this paper is interested in sampling the feasible execution paths in the control flow graph of the program being tested. For some complex programs, the fraction of feasible paths becomes tiny, ranging in [10 −10, 10 −5]. When relying on the uniform sampling of the program paths, SSST is thus hindered by the nonMarkovian nature of the “feasible path ” concept, due to the longrange dependencies between the program nodes. A divide and generate approach relying on an extended Parikh Map representation is proposed to address this limitation; experimental validation on realworld and artificial problems demonstrates gains of orders of magnitude compared to the state of the art. 1
Approximate Structural Consistency
"... Abstract. We consider documents as words and trees on some alphabet Σ and study how to compare them with some regular schemas on an alphabet Σ′. Given an input document I, we decide if it may be transformed into a document J which is εclose to some target schema T: we show that this approximate d ..."
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Abstract. We consider documents as words and trees on some alphabet Σ and study how to compare them with some regular schemas on an alphabet Σ′. Given an input document I, we decide if it may be transformed into a document J which is εclose to some target schema T: we show that this approximate decision problem can be efficiently solved. In the simple case where the transformation is the identity, we describe an approximate algorithm which decides if I is close to a target regular schema (DTD). This property is testable, i.e. can be solved in time independent of the size of the input document, by just sampling I. In the general case, the Structural Consistency decides if there is a transducer T with at most m states such that I is εclose to I ′ and his image T (I ′) is both close to T and of size comparable to the size of I. We show that Structural Consistency is also testable, i.e. can be solved by sampling I. 1
Contents
, 2010
"... Model Checking and Testing are two areas with a similar goal: to verify that a system satisfies a property. They start with different hypothesis on the systems and develop many techniques with different notions of approximation, as an exact verification may be computationally too hard. We present so ..."
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Model Checking and Testing are two areas with a similar goal: to verify that a system satisfies a property. They start with different hypothesis on the systems and develop many techniques with different notions of approximation, as an exact verification may be computationally too hard. We present some of notions of approximation with their Logic and Statistics backgrounds, which yield several techniques
Approximate Schemas, SourceConsistency and Query Answering
"... We use the Edit distance with Moves on words and trees and say that two regular (tree) languages are "close if every word (tree) of one language is "close to the other. A transducer model is introduced to compare tree languages (schemas) with dierent alphabets and attributes. Using the s ..."
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We use the Edit distance with Moves on words and trees and say that two regular (tree) languages are "close if every word (tree) of one language is "close to the other. A transducer model is introduced to compare tree languages (schemas) with dierent alphabets and attributes. Using the statistical embedding of [8], we show that SourceConsistency and Approximate Query Answering are testable on words and trees, i.e. can be approximately decided within " by only looking at a constant fraction of the input. 1
Streaming Property Testing of Visibly Pushdown Languages∗
"... In the context of language recognition, we demonstrate the superiority of streaming property testers against streaming algorithms and property testers, when they are not combined. Initiated by Feigenbaum et al, a streaming property tester is a streaming algorithm recognizing a language under the pro ..."
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In the context of language recognition, we demonstrate the superiority of streaming property testers against streaming algorithms and property testers, when they are not combined. Initiated by Feigenbaum et al, a streaming property tester is a streaming algorithm recognizing a language under the property testing approximation: it must distinguish inputs of the language from those that are εfar from it, while using the smallest possible memory (rather than limiting its number of input queries). Our main result is a streaming εproperty tester for visibly pushdown languages (VPL) with onesided error using memory space poly((log n)/ε). This constructions relies on a new (nonstreaming) property tester for weighted regular languages based on a previous tester by Alon et al. We provide a simple application of this tester for streaming testing special cases of instances of VPL that are already hard for both streaming algorithms and property testers. Our main algorithm is a combination of an original simulation of visibly pushdown automata using a stack with small height but possible items of linear size. In a second step, those items are replaced by small sketches. Those sketches relies on a notion of suffixsampling we introduce. This sampling is the key idea connecting our streaming tester algorithm to property testers. ∗Partially supported by the French ANR projects ANR12BS02005 (RDAM) and ANR14CE250017 (AGREG)