This paper presents a new static analysis for deriving upper bounds on the expected resource consumption of probabilistic programs. The analysis is fully automatic and derives symbolic bounds that are multivariate polynomials in the inputs. The new technique combines manual state-of-theart reasoning techniques for probabilistic programs with an effective method for automatic resource-bound analysis of deterministic programs. It can be seen as both, an extension of automatic amortized resource analysis (AARA) to probabilistic programs and an automation of manual reasoning for probabilistic programs that is based on weakest preconditions. An advantage of the technique is that it combines the clarity and compositionality of a weakest-precondition calculus with the efficient automation of AARA. As a result, bound inference can be reduced to off-the-shelf LP solving in many cases and automatically-derived bounds can be interactively extended with standard program logics if the automation fails. Building on existing work, the soundness of the analysis is proved with respect to an operational semantics that is based on Markov decision processes. The effectiveness of the technique is demonstrated with a prototype implementation that is used to automatically analyze 39 challenging probabilistic programs and randomized algorithms. Experiments indicate that the derived constant factors in the bounds are very precise and even optimal for some programs.CCS Concepts · Software and its engineering → General programming languages; · Social and professional topics → History of programming languages;

This paper presents a new static analysis for deriving upper bounds on the expected resource consumption of probabilistic programs. The analysis is fully automatic and derives symbolic bounds that are multivariate polynomials of the inputs. The new technique combines manual state-of-theart reasoning techniques for probabilistic programs with an effective method for automatic resource-bound analysis of deterministic programs. It can be seen as both, an extension of automatic amortized resource analysis (AARA) to probabilistic programs and an automation of manual reasoning for probabilistic programs that is based on weakest preconditions. An advantage of the technique is that it combines the clarity and compositionality of a weakest-precondition calculus with the efficient automation of AARA. As a result, bound inference can be reduced to off-the-shelf LP solving in many cases and automatically-derived bounds can be interactively extended with standard program logics if the automation fails. Building on existing work, the soundness of the analysis is proved with respect to an operational semantics that is based on Markov decision processes. The effectiveness of the technique is demonstrated with a prototype implementation that is used to automatically analyze 39 challenging probabilistic programs and randomized algorithms. Experimental results indicate that the derived constant factors in the bounds are very precise and even optimal for many programs.

Abstract-Side channel attacks have been used to extract critical data such as encryption keys and confidential user data in a variety of adversarial settings. In practice, this threat is addressed by adhering to a constant-time programming discipline, which imposes strict constraints on the way in which programs are written. This introduces an additional hurdle for programmers faced with the already difficult task of writing secure code, highlighting the need for solutions that give the same source-level guarantees while supporting more natural programming models.We propose a novel type system for verifying that programs correctly implement constant-resource behavior. Our type system extends recent work on automatic amortized resource analysis (AARA), a set of techniques that automatically derive provable upper bounds on the resource consumption of programs. We devise new techniques that build on the potential method to achieve compositionality, precision, and automation.A strict global requirement that a program always maintains constant resource usage is too restrictive for most practical applications. It is sufficient to require that the program's resource behavior remain constant with respect to an attacker who is only allowed to observe part of the program's state and behavior. To account for this, our type system incorporates information flow tracking into its resource analysis. This allows our system to certify programs that need to violate the constanttime requirement in certain cases, as long as doing so does not leak confidential information to attackers. We formalize this guarantee by defining a new notion of resource-aware noninterference, and prove that our system enforces it.Finally, we show how our type inference algorithm can be used to synthesize a constant-time implementation from one that cannot be verified as secure, effectively repairing insecure programs automatically. We also show how a second novel AARA system that computes lower bounds on resource usage can be used to derive quantitative bounds on the amount of information that a program leaks through its resource use. We implemented each of these systems in Resource Aware ML, and show that it can be applied to verify constant-time behavior in a number of applications including encryption and decryption routines, database queries, and other resourceaware functionality.

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Abstract-Transaction-level modeling with SystemC has been very successful in describing the behavior of embedded systems by providing high-level executable models, in which many of them have an inherent probabilistic behavior, i.e., random data, unreliable components. It is crucial to evaluate the quantitative and qualitative analysis of the probability of the system properties. Such analysis can be conducted by constructing a formal model of the system and using probabilistic model checking. However, this method is infeasible for large and complex systems due to the state space explosion. In this paper, we demonstrate the successful use of statistical model checking to carry out such analysis directly from large SystemC models and allows designers to express a wide range of useful properties.