Related papers: Modular Verification for Almost-Sure Termination o…
Recently, there has been an increasing interest in the bottom-up evaluation of the semantics of logic programs with complex terms. The presence of function symbols in the program may render the ground instantiation infinite, and finiteness…
We give rates of convergence in the almost sure invariance principle for sums of dependent random variables with semi exponential tails, whose coupling coefficients decrease at a subexponential rate. We show that the rates in the strong…
Lexicographic Ranking SuperMartingale (LexRSM) is a probabilistic extension of Lexicographic Ranking Function (LexRF), which is a widely accepted technique for verifying program termination. In this paper, we are the first to propose sound…
Properties such as provable security and correctness for randomized programs are naturally expressed relationally as approximate equivalences. As a result, a number of relational program logics have been developed to reason about such…
Deciding in an efficient way weak probabilistic bisimulation in the context of Probabilistic Automata is an open problem for about a decade. In this work we close this problem by proposing a procedure that checks in polynomial time the…
We report on work in progress on automatic procedures for proving properties of programs written in higher-order functional languages. Our approach encodes higher-order programs directly as first-order SMT problems over Horn clauses. It is…
It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…
Hybrid systems, and Piecewise Deterministic Markov Processes in particular, are widely used to model and numerically study systems exhibiting multiple time scales in biochemical reaction kinetics and related areas. In this paper an almost…
Verification of higher-order probabilistic programs is a challenging problem. We present a verification method that supports several quantitative properties of higher-order probabilistic programs. Usually, extending verification methods to…
This paper considers a stochastic approximation algorithm, with decreasing step size and martingale difference noise. Under very mild assumptions, we prove the non convergence of this process toward a certain class of repulsive sets for the…
We report on intermediate results of our research on reasoning about liveness properties in addition to deep correctness properties for an imperative, concurrent programming language with a higher-order store. At present, we focus on one…
We study the almost sure convergence of the Stochastic Approximation algorithm to the fixed point $x^\star$ of a nonlinear operator under a negative drift condition and a general noise sequence with finite $p$-th moment for some $p > 1$.…
Probabilistic programming is an approach to reasoning under uncertainty by encoding inference problems as programs. In order to solve these inference problems, probabilistic programming languages (PPLs) employ different inference…
We show on theoretical grounds that, even in the presence of noise, probabilistic measurement strategies (which have a certain probability of failure or abstention) can provide, upon a heralded successful outcome, estimates with a precision…
Many programs allow the user to input data several times during its execution. If the program runs forever the user may input data infinitely often. A program terminates if it terminates no matter what the user does. We discuss various ways…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…
Numerical software are widely used in safety-critical systems such as aircrafts, satellites, car engines and so on, facilitating dynamics control of such systems in real time, it is therefore absolutely necessary to verify their…
In semidefinite programming (SDP), unlike in linear programming, Farkas' lemma may fail to prove infeasibility. Here we obtain an exact, short certificate of infeasibility in SDP by an elementary approach: we reformulate any semidefinite…
We argue that verification of recursive programs by means of the assertional method of C.A.R. Hoare can be conceptually simplified using a modular reasoning. In this approach some properties of the program are established first and…