67 research outputs found
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
Data-Flow Analysis for Multi-Core Computing Systems: A Reminder to Reverse Data-Flow Analysis
The increasing demands for highly performant, proven correct, easily
maintainable, extensible programs together with the continuous
growth of real-world programs strengthen the pressure for powerful and
scalable program analyses for program development and code
generation. Multi-core computing systems offer new chances for
enhancing the scalability of program analyses, if the additional
computing power offered by these systems can be used
effectively. This, however, poses new challenges on the analysis
side. In principle, it requires program analyses which can be easily
parallelized and mapped to multi-core architectures. In this paper we
remind to reverse data-flow analysis, which has been introduced
and investigated in the context of demand-driven data-flow analysis,
as one such class of program analyses which is particularly suitable
for this
Faster Algorithms for Weighted Recursive State Machines
Pushdown systems (PDSs) and recursive state machines (RSMs), which are
linearly equivalent, are standard models for interprocedural analysis. Yet RSMs
are more convenient as they (a) explicitly model function calls and returns,
and (b) specify many natural parameters for algorithmic analysis, e.g., the
number of entries and exits. We consider a general framework where RSM
transitions are labeled from a semiring and path properties are algebraic with
semiring operations, which can model, e.g., interprocedural reachability and
dataflow analysis problems.
Our main contributions are new algorithms for several fundamental problems.
As compared to a direct translation of RSMs to PDSs and the best-known existing
bounds of PDSs, our analysis algorithm improves the complexity for
finite-height semirings (that subsumes reachability and standard dataflow
properties). We further consider the problem of extracting distance values from
the representation structures computed by our algorithm, and give efficient
algorithms that distinguish the complexity of a one-time preprocessing from the
complexity of each individual query. Another advantage of our algorithm is that
our improvements carry over to the concurrent setting, where we improve the
best-known complexity for the context-bounded analysis of concurrent RSMs.
Finally, we provide a prototype implementation that gives a significant
speed-up on several benchmarks from the SLAM/SDV project
Generating analyzers with PAG
To produce high qualitiy code, modern compilers use global optimization algorithms based on it abstract interpretation. These algorithms are rather complex; their implementation is therfore a non-trivial task and error-prone. However, since thez are based on a common theory, they have large similar parts. We conclude that analyzer writing better should be replaced with analyzer generation. We present the tool sf PAG that has a high level functional input language to specify data flow analyses. It offers th specifications of even recursive data structures and is therfore not limited to bit vector problems. sf PAG generates efficient analyzers wich can be easily integrated in existing compilers. The analyzers are interprocedural, they can handle recursive procedures with local variables and higher order functions. sf PAG has successfully been tested by generating several analyzers (e.g. alias analysis, constant propagation, inerval analysis) for an industrial quality ANSI-C and Fortran90 compiler. This technical report consits of two parts; the first introduces the generation system and the second evaluates generated analyzers with respect to their space and time consumption. bf Keywords: data flow analysis, specification and generation of analyzers, lattice specification, abstract syntax specification, interprocedural analysis, compiler construction
Weighted pushdown systems and their application to interprocedural dataflow analysis
AbstractRecently, pushdown systems (PDSs) have been extended to weighted PDSs, in which each transition is labeled with a value, and the goal is to determine the meet-over-all-paths value (for paths that meet a certain criterion). This paper shows how weighted PDSs yield new algorithms for certain classes of interprocedural dataflow-analysis problems
Faster Algorithms for Dynamic Algebraic Queries in Basic RSMs with Constant Treewidth
Interprocedural analysis is at the heart of numerous applications in programming languages, such as alias analysis, constant propagation, and so on. Recursive state machines (RSMs) are standard models for interprocedural analysis. We consider a general framework with RSMs where the transitions are labeled from a semiring and path properties are algebraic with semiring operations. RSMs with algebraic path properties can model interprocedural dataflow analysis problems, the shortest path problem, the most probable path problem, and so on. The traditional algorithms for interprocedural analysis focus on path properties where the starting point is fixed as the entry point of a specific method. In this work, we consider possible multiple queries as required in many applications such as in alias analysis. The study of multiple queries allows us to bring in an important algorithmic distinction between the resource usage of the one-time preprocessing vs for each individual query. The second aspect we consider is that the control flow graphs for most programs have constant treewidth. Our main contributions are simple and implementable algorithms that support multiple queries for algebraic path properties for RSMs that have constant treewidth. Our theoretical results show that our algorithms have small additional one-time preprocessing but can answer subsequent queries significantly faster as compared to the current algorithmic solutions for interprocedural dataflow analysis. We have also implemented our algorithms and evaluated their performance for performing on-demand interprocedural dataflow analysis on various domains, such as for live variable analysis and reaching definitions, on a standard benchmark set. Our experimental results align with our theoretical statements and show that after a lightweight preprocessing, on-demand queries are answered much faster than the standard existing algorithmic approaches
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