58,193 research outputs found
Generalizing the Paige-Tarjan Algorithm by Abstract Interpretation
The Paige and Tarjan algorithm (PT) for computing the coarsest refinement of
a state partition which is a bisimulation on some Kripke structure is well
known. It is also well known in model checking that bisimulation is equivalent
to strong preservation of CTL, or, equivalently, of Hennessy-Milner logic.
Drawing on these observations, we analyze the basic steps of the PT algorithm
from an abstract interpretation perspective, which allows us to reason on
strong preservation in the context of generic inductively defined (temporal)
languages and of possibly non-partitioning abstract models specified by
abstract interpretation. This leads us to design a generalized Paige-Tarjan
algorithm, called GPT, for computing the minimal refinement of an abstract
interpretation-based model that strongly preserves some given language. It
turns out that PT is a straight instance of GPT on the domain of state
partitions for the case of strong preservation of Hennessy-Milner logic. We
provide a number of examples showing that GPT is of general use. We first show
how a well-known efficient algorithm for computing stuttering equivalence can
be viewed as a simple instance of GPT. We then instantiate GPT in order to
design a new efficient algorithm for computing simulation equivalence that is
competitive with the best available algorithms. Finally, we show how GPT allows
to compute new strongly preserving abstract models by providing an efficient
algorithm that computes the coarsest refinement of a given partition that
strongly preserves the language generated by the reachability operator.Comment: Keywords: Abstract interpretation, abstract model checking, strong
preservation, Paige-Tarjan algorithm, refinement algorith
On the Verification of a WiMax Design Using Symbolic Simulation
In top-down multi-level design methodologies, design descriptions at higher
levels of abstraction are incrementally refined to the final realizations.
Simulation based techniques have traditionally been used to verify that such
model refinements do not change the design functionality. Unfortunately, with
computer simulations it is not possible to completely check that a design
transformation is correct in a reasonable amount of time, as the number of test
patterns required to do so increase exponentially with the number of system
state variables. In this paper, we propose a methodology for the verification
of conformance of models generated at higher levels of abstraction in the
design process to the design specifications. We model the system behavior using
sequence of recurrence equations. We then use symbolic simulation together with
equivalence checking and property checking techniques for design verification.
Using our proposed method, we have verified the equivalence of three WiMax
system models at different levels of design abstraction, and the correctness of
various system properties on those models. Our symbolic modeling and
verification experiments show that the proposed verification methodology
provides performance advantage over its numerical counterpart.Comment: In Proceedings SCSS 2012, arXiv:1307.802
Pac-Learning Recursive Logic Programs: Efficient Algorithms
We present algorithms that learn certain classes of function-free recursive
logic programs in polynomial time from equivalence queries. In particular, we
show that a single k-ary recursive constant-depth determinate clause is
learnable. Two-clause programs consisting of one learnable recursive clause and
one constant-depth determinate non-recursive clause are also learnable, if an
additional ``basecase'' oracle is assumed. These results immediately imply the
pac-learnability of these classes. Although these classes of learnable
recursive programs are very constrained, it is shown in a companion paper that
they are maximally general, in that generalizing either class in any natural
way leads to a computationally difficult learning problem. Thus, taken together
with its companion paper, this paper establishes a boundary of efficient
learnability for recursive logic programs.Comment: See http://www.jair.org/ for any accompanying file
Bisimulations over DLTS in O(m.log n)-time
The well known Hopcroft's algorithm to minimize deterministic complete
automata runs in -time, where is the size of the alphabet and
the number of states. The main part of this algorithm corresponds to the
computation of a coarsest bisimulation over a finite Deterministic Labelled
Transition System (DLTS). By applying techniques we have developed in the case
of simulations, we design a new algorithm which computes the coarsest
bisimulation over a finite DLTS in -time and -space, with
the number of transitions. The underlying DLTS does not need to be complete
and thus: . This new algorithm is much simpler than the two others
found in the literature.Comment: Submitted to DLT'1
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