59,392 research outputs found
Learning Markov Decision Processes for Model Checking
Constructing an accurate system model for formal model verification can be
both resource demanding and time-consuming. To alleviate this shortcoming,
algorithms have been proposed for automatically learning system models based on
observed system behaviors. In this paper we extend the algorithm on learning
probabilistic automata to reactive systems, where the observed system behavior
is in the form of alternating sequences of inputs and outputs. We propose an
algorithm for automatically learning a deterministic labeled Markov decision
process model from the observed behavior of a reactive system. The proposed
learning algorithm is adapted from algorithms for learning deterministic
probabilistic finite automata, and extended to include both probabilistic and
nondeterministic transitions. The algorithm is empirically analyzed and
evaluated by learning system models of slot machines. The evaluation is
performed by analyzing the probabilistic linear temporal logic properties of
the system as well as by analyzing the schedulers, in particular the optimal
schedulers, induced by the learned models.Comment: In Proceedings QFM 2012, arXiv:1212.345
Query Learning with Exponential Query Costs
In query learning, the goal is to identify an unknown object while minimizing
the number of "yes" or "no" questions (queries) posed about that object. A
well-studied algorithm for query learning is known as generalized binary search
(GBS). We show that GBS is a greedy algorithm to optimize the expected number
of queries needed to identify the unknown object. We also generalize GBS in two
ways. First, we consider the case where the cost of querying grows
exponentially in the number of queries and the goal is to minimize the expected
exponential cost. Then, we consider the case where the objects are partitioned
into groups, and the objective is to identify only the group to which the
object belongs. We derive algorithms to address these issues in a common,
information-theoretic framework. In particular, we present an exact formula for
the objective function in each case involving Shannon or Renyi entropy, and
develop a greedy algorithm for minimizing it. Our algorithms are demonstrated
on two applications of query learning, active learning and emergency response.Comment: 15 page
Resolution Trees with Lemmas: Resolution Refinements that Characterize DLL Algorithms with Clause Learning
Resolution refinements called w-resolution trees with lemmas (WRTL) and with
input lemmas (WRTI) are introduced. Dag-like resolution is equivalent to both
WRTL and WRTI when there is no regularity condition. For regular proofs, an
exponential separation between regular dag-like resolution and both regular
WRTL and regular WRTI is given.
It is proved that DLL proof search algorithms that use clause learning based
on unit propagation can be polynomially simulated by regular WRTI. More
generally, non-greedy DLL algorithms with learning by unit propagation are
equivalent to regular WRTI. A general form of clause learning, called
DLL-Learn, is defined that is equivalent to regular WRTL.
A variable extension method is used to give simulations of resolution by
regular WRTI, using a simplified form of proof trace extensions. DLL-Learn and
non-greedy DLL algorithms with learning by unit propagation can use variable
extensions to simulate general resolution without doing restarts.
Finally, an exponential lower bound for WRTL where the lemmas are restricted
to short clauses is shown
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