An Algebraic Framework for Compositional Program Analysis

The purpose of a program analysis is to compute an abstract meaning for a program which approximates its dynamic behaviour. A compositional program analysis accomplishes this task with a divide-and-conquer strategy: the meaning of a program is computed by dividing it into sub-programs, computing their meaning, and then combining the results. Compositional program analyses are desirable because they can yield scalable (and easily parallelizable) program analyses. This paper presents algebraic framework for designing, implementing, and proving the correctness of compositional program analyses. A program analysis in our framework defined by an algebraic structure equipped with sequencing, choice, and iteration operations. From the analysis design perspective, a particularly interesting consequence of this is that the meaning of a loop is computed by applying the iteration operator to the loop body. This style of compositional loop analysis can yield interesting ways of computing loop invariants that cannot be defined iteratively. We identify a class of algorithms, the so-called path-expression algorithms [Tarjan1981,Scholz2007], which can be used to efficiently implement analyses in our framework. Lastly, we develop a theory for proving the correctness of an analysis by establishing an approximation relationship between an algebra defining a concrete semantics and an algebra defining an analysis.Comment: 15 page

Expression-based aliasing for OO-languages

Alias analysis has been an interesting research topic in verification and optimization of programs. The undecidability of determining whether two expressions in a program may reference to the same object is the main source of the challenges raised in alias analysis. In this paper we propose an extension of a previously introduced alias calculus based on program expressions, to the setting of unbounded program executions s.a. infinite loops and recursive calls. Moreover, we devise a corresponding executable specification in the K-framework. An important property of our extension is that, in a non-concurrent setting, the corresponding alias expressions can be over-approximated in terms of a notion of regular expressions. This further enables us to show that the associated K-machinery implements an algorithm that always stops and provides a sound over-approximation of the "may aliasing" information, where soundness stands for the lack of false negatives. As a case study, we analyze the integration and further applications of the alias calculus in SCOOP. The latter is an object-oriented programming model for concurrency, recently formalized in Maude; K-definitions can be compiled into Maude for execution

Safe Automated Refactoring for Intelligent Parallelization of Java 8 Streams

Streaming APIs are becoming more pervasive in mainstream Object-Oriented programming languages and platforms. For example, the Stream API introduced in Java 8 allows for functional-like, MapReduce-style operations in processing both finite, e.g., collections, and infinite data structures. However, using this API efficiently involves subtle considerations such as determining when it is best for stream operations to run in parallel, when running operations in parallel can be less efficient, and when it is safe to run in parallel due to possible lambda expression side-effects. Also, streams may not run all operations in parallel depending on particular collectors used in reductions. In this paper, we present an automated refactoring approach that assists developers in writing efficient stream code in a semantics-preserving fashion. The approach, based on a novel data ordering and typestate analysis, consists of preconditions and transformations for automatically determining when it is safe and possibly advantageous to convert sequential streams to parallel, unorder or de-parallelize already parallel streams, and optimize streams involving complex reductions. The approach was implemented as a plug-in to the popular Eclipse IDE, uses the WALA and SAFE analysis frameworks, and was evaluated on 11 Java projects consisting of ∼642K lines of code. We found that 57 of 157 candidate streams (36.31%) were refactorable, and an average speedup of 3.49 on performance tests was observed. The results indicate that the approach is useful in optimizing stream code to their full potential

Systematic Approaches to Advanced Information Flow Analysis – and Applications to Software Security

In dieser Arbeit berichte ich über Anwendungen von Slicing und Programmabhängigkeitsgraphen (PAG) in der Softwaresicherheit. Außerdem schlage ich ein Analyse-Rahmenwerk vor, welches Datenflussanalyse auf Kontrollflussgraphen und Slicing auf Programmabhängigkeitsgraphen verallgemeinert. Mit einem solchen Rahmenwerk lassen sich neue PAG-basierte Analysen systematisch ableiten, die über Slicing hinausgehen. Die Hauptthesen meiner Arbeit lauten wie folgt: (1) PAG-basierte Informationsflusskontrolle ist nützlich, praktisch anwendbar und relevant. (2) Datenflussanalyse kann systematisch auf Programmabhängigkeitsgraphen angewendet werden. (3) Datenflussanalyse auf Programmabhängigkeitsgraphen ist praktisch durchführbar

IST Austria Thesis

This dissertation focuses on algorithmic aspects of program verification, and presents modeling and complexity advances on several problems related to the static analysis of programs, the stateless model checking of concurrent programs, and the competitive analysis of real-time scheduling algorithms. Our contributions can be broadly grouped into five categories. Our first contribution is a set of new algorithms and data structures for the quantitative and data-flow analysis of programs, based on the graph-theoretic notion of treewidth. It has been observed that the control-flow graphs of typical programs have special structure, and are characterized as graphs of small treewidth. We utilize this structural property to provide faster algorithms for the quantitative and data-flow analysis of recursive and concurrent programs. In most cases we make an algebraic treatment of the considered problem, where several interesting analyses, such as the reachability, shortest path, and certain kind of data-flow analysis problems follow as special cases. We exploit the constant-treewidth property to obtain algorithmic improvements for on-demand versions of the problems, and provide data structures with various tradeoffs between the resources spent in the preprocessing and querying phase. We also improve on the algorithmic complexity of quantitative problems outside the algebraic path framework, namely of the minimum mean-payoff, minimum ratio, and minimum initial credit for energy problems. Our second contribution is a set of algorithms for Dyck reachability with applications to data-dependence analysis and alias analysis. In particular, we develop an optimal algorithm for Dyck reachability on bidirected graphs, which are ubiquitous in context-insensitive, field-sensitive points-to analysis. Additionally, we develop an efficient algorithm for context-sensitive data-dependence analysis via Dyck reachability, where the task is to obtain analysis summaries of library code in the presence of callbacks. Our algorithm preprocesses libraries in almost linear time, after which the contribution of the library in the complexity of the client analysis is (i)~linear in the number of call sites and (ii)~only logarithmic in the size of the whole library, as opposed to linear in the size of the whole library. Finally, we prove that Dyck reachability is Boolean Matrix Multiplication-hard in general, and the hardness also holds for graphs of constant treewidth. This hardness result strongly indicates that there exist no combinatorial algorithms for Dyck reachability with truly subcubic complexity. Our third contribution is the formalization and algorithmic treatment of the Quantitative Interprocedural Analysis framework. In this framework, the transitions of a recursive program are annotated as good, bad or neutral, and receive a weight which measures the magnitude of their respective effect. The Quantitative Interprocedural Analysis problem asks to determine whether there exists an infinite run of the program where the long-run ratio of the bad weights over the good weights is above a given threshold. We illustrate how several quantitative problems related to static analysis of recursive programs can be instantiated in this framework, and present some case studies to this direction. Our fourth contribution is a new dynamic partial-order reduction for the stateless model checking of concurrent programs. Traditional approaches rely on the standard Mazurkiewicz equivalence between traces, by means of partitioning the trace space into equivalence classes, and attempting to explore a few representatives from each class. We present a new dynamic partial-order reduction method called the Data-centric Partial Order Reduction (DC-DPOR). Our algorithm is based on a new equivalence between traces, called the observation equivalence. DC-DPOR explores a coarser partitioning of the trace space than any exploration method based on the standard Mazurkiewicz equivalence. Depending on the program, the new partitioning can be even exponentially coarser. Additionally, DC-DPOR spends only polynomial time in each explored class. Our fifth contribution is the use of automata and game-theoretic verification techniques in the competitive analysis and synthesis of real-time scheduling algorithms for firm-deadline tasks. On the analysis side, we leverage automata on infinite words to compute the competitive ratio of real-time schedulers subject to various environmental constraints. On the synthesis side, we introduce a new instance of two-player mean-payoff partial-information games, and show how the synthesis of an optimal real-time scheduler can be reduced to computing winning strategies in this new type of games