Data flow analysis applied to optimize generic workflow problems

The compiler process, the one that transforms a program in a high level language into assembly or binary code, is a much elaborated process that mixes several powerful technologies, some of them developed specifically for this area. Nowadays, compilers are highly developed systems that can analyze and improve quite efficiently the source code, profiting from all the potential of the new processor architectures. This paper introduces a common type of analysis - the Data Flow Analysis – that is used to compute flow-sensitive information about programs, whose results are essential to produce many code optimizations. It is also argued that the problem of analyzing the data flow in software programs has many similarities with the problems found in industrial engineering; planning and management. As consequence, it is possible to apply analysis and optimization techniques used by compilers in these areas

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

Regular Path Clauses and Their Application in Solving Loops

A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such as cost, on successive loop iterations. Recurrence solvers are capable of computing closed forms for some recurrences, thus deriving precise relationships capturing the complete loop execution. However, many recurrences extracted from loops cannot be solved, due to their having multiple recursive cases or multiple arguments. In the literature, several techniques for approximating the solution of unsolvable recurrences have been proposed. The approach presented in this paper is to define transformations based on regular path expressions and loop counters that (i) transform multi-path loops to single-path loops, giving rise to recurrences with a single recursive case, and (ii) transform multi-argument recurrences to single-argument recurrences, thus enabling the use of recurrence solvers on the transformed recurrences. Using this approach, precise solutions can sometimes be obtained that are not obtained by approximation methods

Sparq2l:towards support for subgraph extraction queries in rdf databases

Many applications in analytical domains often have the need to “connect the dots ” i.e., query about the structure of data. In bioinformatics for example, it is typical to want to query about interactions between proteins. The aim of such queries is to “extract ” relationships between entities i.e. paths from a data graph. Often, such queries will specify certain constraints that qualifying results must satisfy e.g. paths involving a set of mandatory nodes. Unfortunately, most present day Semantic Web query languages including the current draft of the anticipated recommendation SPARQL, lack the ability to express queries about arbitrary path structures in data. In addition, many systems that support some limited form of path queries rely on main memory graph algorithms limiting their applicability to very large scale graphs. In this paper, we present an approach for supporting Path Extraction queries. Our proposal comprises (i) a query language SPARQ2L which extends SPARQL with path variables and path variable constraint expressions, and (ii) a novel query evaluation framework based on efficient algebraic techniques for solving path problems which allows for path queries to be efficiently evaluated on disk resident RDF graphs. The effectiveness of our proposal is demonstrated by a performance evaluation of our approach on both real world and synthetic datasets

Incremental Low-High Orders of Directed Graphs and Applications

A flow graph G = (V, E, s) is a directed graph with a distinguished start vertex s. The dominator tree D of G is a tree rooted at s, such that a vertex v is an ancestor of a vertex w if and only if all paths from s to w include v. The dominator tree is a central tool in program optimization and code generation, and has many applications in other diverse areas including constraint programming, circuit testing, biology, and in algorithms for graph connectivity problems. A low-high order of G is a preorder d of D that certifies the correctness of D, and has further applications in connectivity and path-determination problems. In this paper we consider how to maintain efficiently a low-high order of a flow graph incrementally under edge insertions. We present algorithms that run in O(mn) total time for a sequence of edge insertions in a flow graph with n vertices, where m is the total number of edges after all insertions. These immediately provide the first incremental certifying algorithms for maintaining the dominator tree in O(mn) total time, and also imply incremental algorithms for other problems. Hence, we provide a substantial improvement over the O(m^2) straightforward algorithms, which recompute the solution from scratch after each edge insertion. Furthermore, we provide efficient implementations of our algorithms and conduct an extensive experimental study on real-world graphs taken from a variety of application areas. The experimental results show that our algorithms perform very well in practice