8,555 research outputs found
On Verifying Complex Properties using Symbolic Shape Analysis
One of the main challenges in the verification of software systems is the
analysis of unbounded data structures with dynamic memory allocation, such as
linked data structures and arrays. We describe Bohne, a new analysis for
verifying data structures. Bohne verifies data structure operations and shows
that 1) the operations preserve data structure invariants and 2) the operations
satisfy their specifications expressed in terms of changes to the set of
objects stored in the data structure. During the analysis, Bohne infers loop
invariants in the form of disjunctions of universally quantified Boolean
combinations of formulas. To synthesize loop invariants of this form, Bohne
uses a combination of decision procedures for Monadic Second-Order Logic over
trees, SMT-LIB decision procedures (currently CVC Lite), and an automated
reasoner within the Isabelle interactive theorem prover. This architecture
shows that synthesized loop invariants can serve as a useful communication
mechanism between different decision procedures. Using Bohne, we have verified
operations on data structures such as linked lists with iterators and back
pointers, trees with and without parent pointers, two-level skip lists, array
data structures, and sorted lists. We have deployed Bohne in the Hob and Jahob
data structure analysis systems, enabling us to combine Bohne with analyses of
data structure clients and apply it in the context of larger programs. This
report describes the Bohne algorithm as well as techniques that Bohne uses to
reduce the ammount of annotations and the running time of the analysis
OPE and a low-energy theorem in QCD-like theories
We verify, both perturbatively and nonperturbatively asymptotically in the
ultraviolet (UV), a special case of a low-energy theorem of the NSVZ type in
QCD-like theories, recently derived in arXiv:1701.07833, that relates the
logarithmic derivative with respect to the gauge coupling, or the logarithmic
derivative with respect to the renormalization-group (RG) invariant scale, of
an -point correlator of local operators in one side to an -point
correlator with the insertion of at zero momentum in the other side.
Our computation involves the operator product expansion (OPE) of the scalar
glueball operator, , in massless QCD, worked out perturbatively in
arXiv:1209.1516 -- and in its RG-improved form in the present paper -- by means
of which we extract both the perturbative divergences and the nonperturbative
UV asymptotics in both sides. We also discuss the role of the contact terms in
the OPE, both finite and divergent, discovered some years ago in
arXiv:1209.1516, in relation to the low-energy theorem. Besides, working the
other way around by assuming the low-energy theorem for any 2-point correlator
of a multiplicatively renormalizable gauge-invariant operator, we compute in a
massless QCD-like theory the corresponding perturbative OPE to the order of
and nonperturbative asymptotics. The low-energy theorem has a number of
applications: to the renormalization in asymptotically free QCD-like theories,
both perturbatively and nonperturbatively in the large- 't Hooft and
Veneziano expansions, and to the way the open/closed string duality may or may
not be realized in the would-be solution by canonical string theories for
QCD-like theories, both perturbatively and in the 't Hooft large- expansion.
Our computations will also enter further developments based on the low-energy
theorem.Comment: Some arguments extended and minor typos corrected, paper as published
in JHE
On higher holonomy invariants in higher gauge theory II
This is the second of a series of two technical papers devoted to the
analysis of holonomy invariants in strict higher gauge theory with end
applications in higher Chern--Simons theory. We provide a definition of trace
over a crossed module such to yield surface knot invariants upon application to
2-holonomies. We show further that the properties of the trace are best
described using the theory quandle crossed modules.Comment: Latex, 34 pages, no figure
A mechanized proof of loop freedom of the (untimed) AODV routing protocol
The Ad hoc On-demand Distance Vector (AODV) routing protocol allows the nodes
in a Mobile Ad hoc Network (MANET) or a Wireless Mesh Network (WMN) to know
where to forward data packets. Such a protocol is 'loop free' if it never leads
to routing decisions that forward packets in circles. This paper describes the
mechanization of an existing pen-and-paper proof of loop freedom of AODV in the
interactive theorem prover Isabelle/HOL. The mechanization relies on a novel
compositional approach for lifting invariants to networks of nodes. We exploit
the mechanization to analyse several improvements of AODV and show that
Isabelle/HOL can re-establish most proof obligations automatically and identify
exactly the steps that are no longer valid.Comment: The Isabelle/HOL source files, and a full proof document, are
available in the Archive of Formal Proofs, at
http://afp.sourceforge.net/entries/AODV.shtm
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