102 research outputs found
Model Checking Concurrent Programs with Nondeterminism and Randomization
For concurrent probabilistic programs having process-level nondeterminism, it is often necessary to restrict the class of schedulers that resolve nondeterminism to obtain sound and precise model checking algorithms. In this paper, we introduce two classes of schedulers called view consistent and locally Markovian schedulers and consider the model checking problem of concurrent, probabilistic programs under these alternate semantics. Specifically, given a B"{u}chi automaton , a threshold in , and a concurrent program , the model checking problem asks if the measure of computations of that satisfy is at least , under all view consistent (or locally Markovian) schedulers. We give precise complexity results for the model checking problem (for different classes of B"{u}chi automata specifications) and contrast it with the complexity under the standard semantics that considers all schedulers
Deciding Differential Privacy of Online Algorithms with Multiple Variables
We consider the problem of checking the differential privacy of online
randomized algorithms that process a stream of inputs and produce outputs
corresponding to each input. This paper generalizes an automaton model called
DiP automata (See arXiv:2104.14519) to describe such algorithms by allowing
multiple real-valued storage variables. A DiP automaton is a parametric
automaton whose behavior depends on the privacy budget . An automaton
will be said to be differentially private if, for some , the
automaton is -differentially private for all values of
. We identify a precise characterization of the class of all
differentially private DiP automata. We show that the problem of determining if
a given DiP automaton belongs to this class is PSPACE-complete. Our PSPACE
algorithm also computes a value for when the given automaton is
differentially private. The algorithm has been implemented, and experiments
demonstrating its effectiveness are presented
Finding symmetry in models of concurrent systems by static channel diagram analysis
Over the last decade there has been much interest in exploiting symmetry to combat the state explosion problem in model checking. Although symmetry in a model often arises as a result of symmetry in the topology of the system being modelled, most model checkers which exploit structural symmetry are limited to topologies which exhibit total symmetries, such as stars and cliques. We define the static channel diagram of a concurrent, message passing program, and show that under certain restrictions there is a correspondence between symmetries of the static channel diagram of a program and symmetries of the Kripke structure associated with the program. This allows the detection, and potential exploitation, of structural symmetry in systems with arbitrary topologies. Our method of symmetry detection can handle mobile systems where channel references are passed on channels, resulting in a dynamic communication structure. We illustrate our results with an example using the Promela modelling language
Power of Randomization in Automata on Infinite Strings
Probabilistic B\"uchi Automata (PBA) are randomized, finite state automata
that process input strings of infinite length. Based on the threshold chosen
for the acceptance probability, different classes of languages can be defined.
In this paper, we present a number of results that clarify the power of such
machines and properties of the languages they define. The broad themes we focus
on are as follows. We present results on the decidability and precise
complexity of the emptiness, universality and language containment problems for
such machines, thus answering questions central to the use of these models in
formal verification. Next, we characterize the languages recognized by PBAs
topologically, demonstrating that though general PBAs can recognize languages
that are not regular, topologically the languages are as simple as
\omega-regular languages. Finally, we introduce Hierarchical PBAs, which are
syntactically restricted forms of PBAs that are tractable and capture exactly
the class of \omega-regular languages
Interactive Termination Proofs Using Termination Cores
Abstract. Recent advances in termination analysis have yielded new methods and tools that are highly automatic. However, when they fail, even experts have difficulty understanding why and determining how to proceed. In this paper, we address the issue of building termination analysis engines that are both highly automatic and easy to use in an interactive setting. We consider the problem in the context of ACL2, which has a first-order, functional programming language. We introduce the notion of a termination core, a simplification of the program under consideration which consists of a single loop that the termination engine cannot handle. We show how to extend the Size Change Termination (SCT) algorithm so that it generates termination cores when it fails to prove termination, with no increase to its complexity. We show how to integrate this into the Calling Context Graph (CCG) termination analysis, a powerful SCT-based automatic termination analysis that is part of the ACL2 Sedan. We also present several new, convenient ways of allowing users to interface with the CCG analysis, in order to guide it to a termination proof.
Minimization of Communication Cost Through Caching in Mobile Environments
Users of mobile computers will soon have online access to a large number of databases via wireless networks. Because of limited bandwidth, wireless communication is more expensive than wire communication. In this paper we present and analyze various static and dynamic data allocation methods. The objective is to optimize the communication cost between a mobile computer and the stationary computer that stores the online database. Analysis is performed in two cost models. One is connection (or time) based, as in cellular telephones, where the user is charged per minute of connection. The other is message based, as in packet radio networks, where the user is charged per message. Our analysis addresses both, the average case and the worst case for determining the best allocation method. A preliminary version of this paper has appeared in the Proceedings of the ACM-SIGMOD, May 1994, Minneapolis, Minnesota. This research was supported in part by Grants NSF IRI-9224605, NSF IRI-9408750, DAR..
Triggers on Database Histories
this paper, they are incomparable with respect to expressive power. Specifically, there are variants of TL that are more expressive than variants of EE and FOL, and vice versa. Particularly, it can be shown that a variant of TL without global variables is equivalent in expressive power to EE
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