Bounded Expectations: Resource Analysis for Probabilistic Programs

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-the-art 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. 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

Type-Based Analysis of Logarithmic Amortised Complexity

We introduce a novel amortised resource analysis couched in a type-and-effect system. Our analysis is formulated in terms of the physicist's method of amortised analysis, and is potential-based. The type system makes use of logarithmic potential functions and is the first such system to exhibit *logarithmic amortised complexity*. With our approach we target the automated analysis of self-adjusting data structures, like splay trees, which so far have only manually been analysed in the literature. In particular, we have implemented a semi-automated prototype, which successfully analyses the zig-zig case of *splaying*, once the type annotations are fixed.Comment: 35 pages. arXiv admin note: text overlap with arXiv:1807.0824

Verifying and Synthesizing Constant-Resource Implementations with Types

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 constant-time 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 resource-aware functionality.Comment: 30, IEEE S&P 201

Amortised Resource Analysis and Typed Polynomial Interpretations

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