Modular verification of procedure equivalence in the presence of memory allocation

For most high level languages, two procedures are equivalent if they transform a pair of isomorphic stores to isomorphic stores. How- ever, tools for modular checking of such equivalence impose a stronger check where isomorphism is strengthened to equality of stores. This re- sults in the inability to prove many interesting program pairs with re- cursion and dynamic memory allocation. In this work, we present RIE, a methodology to modularly establish equivalence of procedures in the presence of memory allocation, cyclic data structures and recursion. Our technique addresses the need for find- ing witnesses to isomorphism with angelic allocation, supports reasoning about equivalent procedures calls when the stores are only locally iso- morphic, and reasoning about changes in the order of procedure calls. We have implemented RIE by encoding it in the Boogie program verifier. We describe the encoding and prove its soundness

Heap Abstractions for Static Analysis

Heap data is potentially unbounded and seemingly arbitrary. As a consequence, unlike stack and static memory, heap memory cannot be abstracted directly in terms of a fixed set of source variable names appearing in the program being analysed. This makes it an interesting topic of study and there is an abundance of literature employing heap abstractions. Although most studies have addressed similar concerns, their formulations and formalisms often seem dissimilar and some times even unrelated. Thus, the insights gained in one description of heap abstraction may not directly carry over to some other description. This survey is a result of our quest for a unifying theme in the existing descriptions of heap abstractions. In particular, our interest lies in the abstractions and not in the algorithms that construct them. In our search of a unified theme, we view a heap abstraction as consisting of two features: a heap model to represent the heap memory and a summarization technique for bounding the heap representation. We classify the models as storeless, store based, and hybrid. We describe various summarization techniques based on k-limiting, allocation sites, patterns, variables, other generic instrumentation predicates, and higher-order logics. This approach allows us to compare the insights of a large number of seemingly dissimilar heap abstractions and also paves way for creating new abstractions by mix-and-match of models and summarization techniques.Comment: 49 pages, 20 figure

The Meaning of Memory Safety

We give a rigorous characterization of what it means for a programming language to be memory safe, capturing the intuition that memory safety supports local reasoning about state. We formalize this principle in two ways. First, we show how a small memory-safe language validates a noninterference property: a program can neither affect nor be affected by unreachable parts of the state. Second, we extend separation logic, a proof system for heap-manipulating programs, with a memory-safe variant of its frame rule. The new rule is stronger because it applies even when parts of the program are buggy or malicious, but also weaker because it demands a stricter form of separation between parts of the program state. We also consider a number of pragmatically motivated variations on memory safety and the reasoning principles they support. As an application of our characterization, we evaluate the security of a previously proposed dynamic monitor for memory safety of heap-allocated data.Comment: POST'18 final versio

On the Complexity of the Equivalence Problem for Probabilistic Automata

Checking two probabilistic automata for equivalence has been shown to be a key problem for efficiently establishing various behavioural and anonymity properties of probabilistic systems. In recent experiments a randomised equivalence test based on polynomial identity testing outperformed deterministic algorithms. In this paper we show that polynomial identity testing yields efficient algorithms for various generalisations of the equivalence problem. First, we provide a randomized NC procedure that also outputs a counterexample trace in case of inequivalence. Second, we show how to check for equivalence two probabilistic automata with (cumulative) rewards. Our algorithm runs in deterministic polynomial time, if the number of reward counters is fixed. Finally we show that the equivalence problem for probabilistic visibly pushdown automata is logspace equivalent to the Arithmetic Circuit Identity Testing problem, which is to decide whether a polynomial represented by an arithmetic circuit is identically zero.Comment: technical report for a FoSSaCS'12 pape