672 research outputs found
Predicate Abstraction with Indexed Predicates
Predicate abstraction provides a powerful tool for verifying properties of
infinite-state systems using a combination of a decision procedure for a subset
of first-order logic and symbolic methods originally developed for finite-state
model checking. We consider models containing first-order state variables,
where the system state includes mutable functions and predicates. Such a model
can describe systems containing arbitrarily large memories, buffers, and arrays
of identical processes. We describe a form of predicate abstraction that
constructs a formula over a set of universally quantified variables to describe
invariant properties of the first-order state variables. We provide a formal
justification of the soundness of our approach and describe how it has been
used to verify several hardware and software designs, including a
directory-based cache coherence protocol.Comment: 27 pages, 4 figures, 1 table, short version appeared in International
Conference on Verification, Model Checking and Abstract Interpretation
(VMCAI'04), LNCS 2937, pages = 267--28
Continuation-Passing C: compiling threads to events through continuations
In this paper, we introduce Continuation Passing C (CPC), a programming
language for concurrent systems in which native and cooperative threads are
unified and presented to the programmer as a single abstraction. The CPC
compiler uses a compilation technique, based on the CPS transform, that yields
efficient code and an extremely lightweight representation for contexts. We
provide a proof of the correctness of our compilation scheme. We show in
particular that lambda-lifting, a common compilation technique for functional
languages, is also correct in an imperative language like C, under some
conditions enforced by the CPC compiler. The current CPC compiler is mature
enough to write substantial programs such as Hekate, a highly concurrent
BitTorrent seeder. Our benchmark results show that CPC is as efficient, while
using significantly less space, as the most efficient thread libraries
available.Comment: Higher-Order and Symbolic Computation (2012). arXiv admin note:
substantial text overlap with arXiv:1202.324
Computation of Iwasawa Lambda invariants for imaginary quadratic fields
A method for computing the Iwasawa lambda invariants of an imaginary quadratic field is developed and used to construct a table of these invariants for discriminants up to 1,000 and primes up to 20,000
[SADE] A Maple package for the Symmetry Analysis of Differential Equations
We present the package SADE (Symmetry Analysis of Differential Equations) for
the determination of symmetries and related properties of systems of
differential equations. The main methods implemented are: Lie, nonclassical,
Lie-B\"acklund and potential symmetries, invariant solutions, first-integrals,
N\"other theorem for both discrete and continuous systems, solution of ordinary
differential equations, reduction of order or dimension using Lie symmetries,
classification of differential equations, Casimir invariants, and the
quasi-polynomial formalism for ODE's (previously implemented in the package
QPSI by the authors) for the determination of quasi-polynomial first-integrals,
Lie symmetries and invariant surfaces. Examples of use of the package are
given
Sciduction: Combining Induction, Deduction, and Structure for Verification and Synthesis
Even with impressive advances in automated formal methods, certain problems
in system verification and synthesis remain challenging. Examples include the
verification of quantitative properties of software involving constraints on
timing and energy consumption, and the automatic synthesis of systems from
specifications. The major challenges include environment modeling,
incompleteness in specifications, and the complexity of underlying decision
problems.
This position paper proposes sciduction, an approach to tackle these
challenges by integrating inductive inference, deductive reasoning, and
structure hypotheses. Deductive reasoning, which leads from general rules or
concepts to conclusions about specific problem instances, includes techniques
such as logical inference and constraint solving. Inductive inference, which
generalizes from specific instances to yield a concept, includes algorithmic
learning from examples. Structure hypotheses are used to define the class of
artifacts, such as invariants or program fragments, generated during
verification or synthesis. Sciduction constrains inductive and deductive
reasoning using structure hypotheses, and actively combines inductive and
deductive reasoning: for instance, deductive techniques generate examples for
learning, and inductive reasoning is used to guide the deductive engines.
We illustrate this approach with three applications: (i) timing analysis of
software; (ii) synthesis of loop-free programs, and (iii) controller synthesis
for hybrid systems. Some future applications are also discussed
On the structure of the Galois group of the maximal pro- extension with restricted ramification over the cyclotomic -extension
Let be the cyclotomic -extension of an algebraic
number field . We denote by a finite set of prime numbers which does not
contain , and the set of primes of lying above .
In the present paper, we will study the structure of the Galois group
of the maximal pro- extension unramified outside
over . We mainly consider the question whether
is a non-abelian free pro- group or not. In the
former part, we treat the case when is an imaginary quadratic field and (here is an odd prime number which does not split in ). In
the latter part, we treat the case when is a totally real field and .Comment: 20 pages, changed several places, added sentences and reference
On the p-adic Leopoldt Transform of a power series
In this paper we give a bound for the Iwasawa lambda invariant of an abelian
number field attached to the cyclotomic Z_p-extension of that field. We also
give some properties of Iwaswa power series attached to p-adic L-functions
On the Expressivity of Minimal Generic Quantification
AbstractWe come back to the initial design of the ∇ quantifier by Miller and Tiu, which we call minimal generic quantification. In the absence of fixed points, it is equivalent to seemingly stronger designs. However, several expected theorems about (co)inductive specifications can not be derived in that setting. We present a refinement of minimal generic quantification that brings the expected expressivity while keeping the minimal semantic, which we claim is useful to get natural adequate specifications. We build on the idea that generic quantification is not a logical connective but one that is defined, like negation in classical logics. This allows us to use the standard (co)induction rule, but obtain much more expressivity than before. We show classes of theorems that can now be derived in the logic, and present a few practical examples
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