1,593 research outputs found
A Backward Analysis for Constraint Logic Programs
One recurring problem in program development is that of understanding how to
re-use code developed by a third party. In the context of (constraint) logic
programming, part of this problem reduces to figuring out how to query a
program. If the logic program does not come with any documentation, then the
programmer is forced to either experiment with queries in an ad hoc fashion or
trace the control-flow of the program (backward) to infer the modes in which a
predicate must be called so as to avoid an instantiation error. This paper
presents an abstract interpretation scheme that automates the latter technique.
The analysis presented in this paper can infer moding properties which if
satisfied by the initial query, come with the guarantee that the program and
query can never generate any moding or instantiation errors. Other applications
of the analysis are discussed. The paper explains how abstract domains with
certain computational properties (they condense) can be used to trace
control-flow backward (right-to-left) to infer useful properties of initial
queries. A correctness argument is presented and an implementation is reported.Comment: 32 page
Transformations of CCP programs
We introduce a transformation system for concurrent constraint programming
(CCP). We define suitable applicability conditions for the transformations
which guarantee that the input/output CCP semantics is preserved also when
distinguishing deadlocked computations from successful ones and when
considering intermediate results of (possibly) non-terminating computations.
The system allows us to optimize CCP programs while preserving their intended
meaning: In addition to the usual benefits that one has for sequential
declarative languages, the transformation of concurrent programs can also lead
to the elimination of communication channels and of synchronization points, to
the transformation of non-deterministic computations into deterministic ones,
and to the crucial saving of computational space. Furthermore, since the
transformation system preserves the deadlock behavior of programs, it can be
used for proving deadlock freeness of a given program wrt a class of queries.
To this aim it is sometimes sufficient to apply our transformations and to
specialize the resulting program wrt the given queries in such a way that the
obtained program is trivially deadlock free.Comment: To appear in ACM TOPLA
Towards an Effective Decision Procedure for LTL formulas with Constraints
This paper presents an ongoing work that is part of a more wide-ranging
project whose final scope is to define a method to validate LTL formulas w.r.t.
a program written in the timed concurrent constraint language tccp, which is a
logic concurrent constraint language based on the concurrent constraint
paradigm of Saraswat. Some inherent notions to tccp processes are
non-determinism, dealing with partial information in states and the monotonic
evolution of the information. In order to check an LTL property for a process,
our approach is based on the abstract diagnosis technique. The concluding step
of this technique needs to check the validity of an LTL formula (with
constraints) in an effective way.
In this paper, we present a decision method for the validity of temporal
logic formulas (with constraints) built by our abstract diagnosis technique.Comment: Part of WLPE 2013 proceedings (arXiv:1308.2055
An Abstract Interpretation Framework for Diagnosis and Verification of Timed Concurrent Constraint Languages
In this thesis, we propose a semantic framework for tccp based on abstract interpretation with the main purpose of formally verifying and debugging tccp programs.
A key point for the efficacy of the resulting methodologies is the adequacy of the concrete semantics. Thus, in this thesis, much effort has been devoted to the development of a suitable small-step denotational semantics for the tccp language to start with.
Our denotational semantics models precisely the small-step behavior of tccp and is suitable to be used within the abstract interpretation framework. Namely, it is defined in a compositional and bottom-up way, it is as condensed as possible (it does not contain
redundant elements), and it is goal-independent (its calculus does not depend on the semantic evaluation of a specific initial agent).
Another contribution of this thesis is the definition (by abstraction of our small-step denotational semantics) of a big-step denotational semantics that abstracts away from the information about the evolution of the state and keeps only the the first and the last (if it exists) state. We show that this big-step semantics is essentially equivalent to the input-output semantics.
In order to fulfill our goal of formally validate tccp programs, we build different approximations of our small-step denotational semantics by using standard abstract interpretation techniques. In this way we obtain debugging and verification tools which are correct by construction. More specifically, we propose two abstract semantics that are used to formally debug tccp programs. The first one approximates the information content of tccp behavioral traces, while the second one approximates our small-step semantics with temporal logic formulas. By applying abstract diagnosis with these abstract semantics we obtain two fully-automatic verification methods for tccp
Abstract Interpretation of Temporal Concurrent Constraint Programs
International audienceTimed Concurrent Constraint Programming (tcc) is a declarative model for concurrency offering a logic for specifying reactive systems, i.e. systems that continuously interact with the environment. The universal tcc formalism (utcc) is an extension of tcc with the abil- ity to express mobility. Here mobility is understood as communication of private names as typically done for mobile systems and security protocols. In this paper we consider the denotational semantics for tcc, and we extend it to a "collecting" semantics for utcc based on closure operators over sequences of constraints. Relying on this semantics, we formalize a general framework for data flow analyses of tcc and utcc programs by abstract inter- pretation techniques. The concrete and abstract semantics we propose are compositional, thus allowing us to reduce the complexity of data flow analyses. We show that our method is sound and parametric with respect to the abstract domain. Thus, different analyses can be performed by instantiating the framework. We illustrate how it is possible to reuse abstract domains previously defined for logic programming to perform, for instance, a groundness analysis for tcc programs. We show the applicability of this analysis in the context of reactive systems. Furthermore, we make also use of the abstract semantics to exhibit a secrecy flaw in a security protocol. We also show how it is possible to make an analysis which may show that tcc programs are suspension free. This can be useful for several purposes, such as for optimizing compilation or for debugging
The Complexity of Relating Quantum Channels to Master Equations
Completely positive, trace preserving (CPT) maps and Lindblad master
equations are both widely used to describe the dynamics of open quantum
systems. The connection between these two descriptions is a classic topic in
mathematical physics. One direction was solved by the now famous result due to
Lindblad, Kossakowski Gorini and Sudarshan, who gave a complete
characterisation of the master equations that generate completely positive
semi-groups. However, the other direction has remained open: given a CPT map,
is there a Lindblad master equation that generates it (and if so, can we find
it's form)? This is sometimes known as the Markovianity problem. Physically, it
is asking how one can deduce underlying physical processes from experimental
observations.
We give a complexity theoretic answer to this problem: it is NP-hard. We also
give an explicit algorithm that reduces the problem to integer semi-definite
programming, a well-known NP problem. Together, these results imply that
resolving the question of which CPT maps can be generated by master equations
is tantamount to solving P=NP: any efficiently computable criterion for
Markovianity would imply P=NP; whereas a proof that P=NP would imply that our
algorithm already gives an efficiently computable criterion. Thus, unless P
does equal NP, there cannot exist any simple criterion for determining when a
CPT map has a master equation description.
However, we also show that if the system dimension is fixed (relevant for
current quantum process tomography experiments), then our algorithm scales
efficiently in the required precision, allowing an underlying Lindblad master
equation to be determined efficiently from even a single snapshot in this case.
Our work also leads to similar complexity-theoretic answers to a related
long-standing open problem in probability theory.Comment: V1: 43 pages, single column, 8 figures. V2: titled changed; added
proof-overview and accompanying figure; 50 pages, single column, 9 figure
The Analysis of Space-Time Structure in QCD Vacuum II: Dynamics of Polarization and Absolute X-Distribution
We propose a framework for quantitative evaluation of dynamical tendency for
polarization in arbitrary random variable that can be decomposed into a pair of
orthogonal subspaces. The method uses measures based on comparisons of given
dynamics to its counterpart with statistically independent components. The
formalism of previously considered X-distributions is used to express the
aforementioned comparisons, in effect putting the former approach on solid
footing. Our analysis leads to definition of a suitable correlation coefficient
with clear statistical meaning. We apply the method to the dynamics induced by
pure-glue lattice QCD in local left-right components of overlap Dirac
eigenmodes. It is found that, in finite physical volume, there exists a
non-zero physical scale in the spectrum of eigenvalues such that eigenmodes at
smaller (fixed) eigenvalues exhibit convex X-distribution (positive
correlation), while at larger eigenvalues the distribution is concave (negative
correlation). This chiral polarization scale thus separates a regime where
dynamics enhances chirality relative to statistical independence from a regime
where it suppresses it, and gives an objective definition to the notion of
"low" and "high" Dirac eigenmode. We propose to investigate whether the
polarization scale remains non-zero in the infinite volume limit, in which case
it would represent a new kind of low energy scale in QCD.Comment: v2: 38 pages, 12 figures, author-preferred version; v3:
journal-preferred versio
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