121,912 research outputs found
Invariant Generation through Strategy Iteration in Succinctly Represented Control Flow Graphs
We consider the problem of computing numerical invariants of programs, for
instance bounds on the values of numerical program variables. More
specifically, we study the problem of performing static analysis by abstract
interpretation using template linear constraint domains. Such invariants can be
obtained by Kleene iterations that are, in order to guarantee termination,
accelerated by widening operators. In many cases, however, applying this form
of extrapolation leads to invariants that are weaker than the strongest
inductive invariant that can be expressed within the abstract domain in use.
Another well-known source of imprecision of traditional abstract interpretation
techniques stems from their use of join operators at merge nodes in the control
flow graph. The mentioned weaknesses may prevent these methods from proving
safety properties. The technique we develop in this article addresses both of
these issues: contrary to Kleene iterations accelerated by widening operators,
it is guaranteed to yield the strongest inductive invariant that can be
expressed within the template linear constraint domain in use. It also eschews
join operators by distinguishing all paths of loop-free code segments. Formally
speaking, our technique computes the least fixpoint within a given template
linear constraint domain of a transition relation that is succinctly expressed
as an existentially quantified linear real arithmetic formula. In contrast to
previously published techniques that rely on quantifier elimination, our
algorithm is proved to have optimal complexity: we prove that the decision
problem associated with our fixpoint problem is in the second level of the
polynomial-time hierarchy.Comment: 35 pages, conference version published at ESOP 2011, this version is
a CoRR version of our submission to Logical Methods in Computer Scienc
Survey on Combinatorial Register Allocation and Instruction Scheduling
Register allocation (mapping variables to processor registers or memory) and
instruction scheduling (reordering instructions to increase instruction-level
parallelism) are essential tasks for generating efficient assembly code in a
compiler. In the last three decades, combinatorial optimization has emerged as
an alternative to traditional, heuristic algorithms for these two tasks.
Combinatorial optimization approaches can deliver optimal solutions according
to a model, can precisely capture trade-offs between conflicting decisions, and
are more flexible at the expense of increased compilation time.
This paper provides an exhaustive literature review and a classification of
combinatorial optimization approaches to register allocation and instruction
scheduling, with a focus on the techniques that are most applied in this
context: integer programming, constraint programming, partitioned Boolean
quadratic programming, and enumeration. Researchers in compilers and
combinatorial optimization can benefit from identifying developments, trends,
and challenges in the area; compiler practitioners may discern opportunities
and grasp the potential benefit of applying combinatorial optimization
A Symbolic Execution Algorithm for Constraint-Based Testing of Database Programs
In so-called constraint-based testing, symbolic execution is a common
technique used as a part of the process to generate test data for imperative
programs. Databases are ubiquitous in software and testing of programs
manipulating databases is thus essential to enhance the reliability of
software. This work proposes and evaluates experimentally a symbolic ex-
ecution algorithm for constraint-based testing of database programs. First, we
describe SimpleDB, a formal language which offers a minimal and well-defined
syntax and seman- tics, to model common interaction scenarios between pro-
grams and databases. Secondly, we detail the proposed al- gorithm for symbolic
execution of SimpleDB models. This algorithm considers a SimpleDB program as a
sequence of operations over a set of relational variables, modeling both the
database tables and the program variables. By inte- grating this relational
model of the program with classical static symbolic execution, the algorithm
can generate a set of path constraints for any finite path to test in the
control- flow graph of the program. Solutions of these constraints are test
inputs for the program, including an initial content for the database. When the
program is executed with respect to these inputs, it is guaranteed to follow
the path with re- spect to which the constraints were generated. Finally, the
algorithm is evaluated experimentally using representative SimpleDB models.Comment: 12 pages - preliminary wor
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