
Fixedpoint elimination in the Intuitionistic Propositional Calculus (extended version)
It is a consequence of existing literature that least and greatest fixed...
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Upper bounds on the graph minor theorem
Lower bounds on the prooftheoretic strength of the graph minor theorem ...
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Certified Roundoff Error Bounds using Bernstein Expansions and Sparse KrivineStengle Representations
Floating point error is a drawback of embedded systems implementation th...
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ConcentrationBound Analysis for Probabilistic Programs and Probabilistic Recurrence Relations
Analyzing probabilistic programs and randomized algorithms are classical...
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Efficient Algorithms for Checking Fast Termination in VASS
Vector Addition Systems with States (VASS) consists of a finite state sp...
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New Subexponential Fewnomial Hypersurface Bounds
Suppose c_1,...,c_n+k are real numbers, {a_1,...,a_n+k}⊂R^n is a set of ...
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Cost Analysis of Nondeterministic Probabilistic Programs
We consider the problem of expected cost analysis over nondeterministic ...
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Quantitative Analysis of Assertion Violations in Probabilistic Programs
In this work, we consider the fundamental problem of deriving quantitative bounds on the probability that a given assertion is violated in a probabilistic program. We provide automated algorithms that obtain both lower and upper bounds on the assertion violation probability in exponential forms. The main novelty of our approach is that we prove new and dedicated fixedpoint theorems which serve as the theoretical basis of our algorithms and enable us to reason about assertion violation bounds in terms of pre and post fixedpoint functions. To synthesize such fixedpoints, we devise algorithms that utilize a wide range of mathematical tools, including repulsing ranking supermartingales, Hoeffding's lemma, Minkowski decompositions, Jensen's inequality, and convex optimization. On the theoretical side, we provide (i) the first automated algorithm for lowerbounds on assertion violation probabilities, (ii) the first complete algorithm for upperbounds of exponential form in affine programs, and (iii) provably and significantly tighter upperbounds than the previous approach of stochastic invariants. On the practical side, we show that our algorithms can handle a wide variety of programs from the literature and synthesize bounds that are several orders of magnitude tighter in comparison with previous approaches.
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