10,497 research outputs found
Model Checking Markov Chains with Actions and State Labels
In the past, logics of several kinds have been proposed for reasoning about discrete- or continuous-time Markov chains. Most of these logics rely on either state labels (atomic propositions) or on transition labels (actions). However, in several applications it is useful to reason about both state-properties and action-sequences. For this purpose, we introduce the logic asCSL which provides powerful means to characterize execution paths of Markov chains with actions and state labels. asCSL can be regarded as an extension of the purely state-based logic asCSL (continuous stochastic logic). \ud
In asCSL, path properties are characterized by regular expressions over actions and state-formulas. Thus, the truth value of path-formulas does not only depend on the available actions in a given time interval, but also on the validity of certain state formulas in intermediate states.\ud
We compare the expressive power of CSL and asCSL and show that even the state-based fragment of asCSL is strictly more expressive than CSL if time intervals starting at zero are employed. Using an automaton-based technique, an asCSL formula and a Markov chain with actions and state labels are combined into a product Markov chain. For time intervals starting at zero we establish a reduction of the model checking problem for asCSL to CSL model checking on this product Markov chain. The usefulness of our approach is illustrated by through an elaborate model of a scalable cellular communication system for which several properties are formalized by means of asCSL-formulas, and checked using the new procedure
History-Register Automata
Programs with dynamic allocation are able to create and use an unbounded
number of fresh resources, such as references, objects, files, etc. We propose
History-Register Automata (HRA), a new automata-theoretic formalism for
modelling such programs. HRAs extend the expressiveness of previous approaches
and bring us to the limits of decidability for reachability checks. The
distinctive feature of our machines is their use of unbounded memory sets
(histories) where input symbols can be selectively stored and compared with
symbols to follow. In addition, stored symbols can be consumed or deleted by
reset. We show that the combination of consumption and reset capabilities
renders the automata powerful enough to imitate counter machines, and yields
closure under all regular operations apart from complementation. We moreover
examine weaker notions of HRAs which strike different balances between
expressiveness and effectiveness.Comment: LMCS (improved version of FoSSaCS
Using Inhabitation in Bounded Combinatory Logic with Intersection Types for Composition Synthesis
We describe ongoing work on a framework for automatic composition synthesis
from a repository of software components. This work is based on combinatory
logic with intersection types. The idea is that components are modeled as typed
combinators, and an algorithm for inhabitation {\textemdash} is there a
combinatory term e with type tau relative to an environment Gamma?
{\textemdash} can be used to synthesize compositions. Here, Gamma represents
the repository in the form of typed combinators, tau specifies the synthesis
goal, and e is the synthesized program. We illustrate our approach by examples,
including an application to synthesis from GUI-components.Comment: In Proceedings ITRS 2012, arXiv:1307.784
Tabling with Sound Answer Subsumption
Tabling is a powerful resolution mechanism for logic programs that captures
their least fixed point semantics more faithfully than plain Prolog. In many
tabling applications, we are not interested in the set of all answers to a
goal, but only require an aggregation of those answers. Several works have
studied efficient techniques, such as lattice-based answer subsumption and
mode-directed tabling, to do so for various forms of aggregation.
While much attention has been paid to expressivity and efficient
implementation of the different approaches, soundness has not been considered.
This paper shows that the different implementations indeed fail to produce
least fixed points for some programs. As a remedy, we provide a formal
framework that generalises the existing approaches and we establish a soundness
criterion that explains for which programs the approach is sound.
This article is under consideration for acceptance in TPLP.Comment: Paper presented at the 32nd International Conference on Logic
Programming (ICLP 2016), New York City, USA, 16-21 October 2016, 15 pages,
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On the Complexity of the Equivalence Problem for Probabilistic Automata
Checking two probabilistic automata for equivalence has been shown to be a
key problem for efficiently establishing various behavioural and anonymity
properties of probabilistic systems. In recent experiments a randomised
equivalence test based on polynomial identity testing outperformed
deterministic algorithms. In this paper we show that polynomial identity
testing yields efficient algorithms for various generalisations of the
equivalence problem. First, we provide a randomized NC procedure that also
outputs a counterexample trace in case of inequivalence. Second, we show how to
check for equivalence two probabilistic automata with (cumulative) rewards. Our
algorithm runs in deterministic polynomial time, if the number of reward
counters is fixed. Finally we show that the equivalence problem for
probabilistic visibly pushdown automata is logspace equivalent to the
Arithmetic Circuit Identity Testing problem, which is to decide whether a
polynomial represented by an arithmetic circuit is identically zero.Comment: technical report for a FoSSaCS'12 pape
Linear Encodings of Bounded LTL Model Checking
We consider the problem of bounded model checking (BMC) for linear temporal
logic (LTL). We present several efficient encodings that have size linear in
the bound. Furthermore, we show how the encodings can be extended to LTL with
past operators (PLTL). The generalised encoding is still of linear size, but
cannot detect minimal length counterexamples. By using the virtual unrolling
technique minimal length counterexamples can be captured, however, the size of
the encoding is quadratic in the specification. We also extend virtual
unrolling to Buchi automata, enabling them to accept minimal length
counterexamples.
Our BMC encodings can be made incremental in order to benefit from
incremental SAT technology. With fairly small modifications the incremental
encoding can be further enhanced with a termination check, allowing us to prove
properties with BMC. Experiments clearly show that our new encodings improve
performance of BMC considerably, particularly in the case of the incremental
encoding, and that they are very competitive for finding bugs. An analysis of
the liveness-to-safety transformation reveals many similarities to the BMC
encodings in this paper. Using the liveness-to-safety translation with
BDD-based invariant checking results in an efficient method to find shortest
counterexamples that complements the BMC-based approach.Comment: Final version for Logical Methods in Computer Science CAV 2005
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