Intensional and Extensional Semantics of Bounded and Unbounded Nondeterminism

We give extensional and intensional characterizations of nondeterministic functional programs: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which compute them. A fundamental result establishes that the extensional and intensional representations of non-deterministic programs are equivalent, by showing how to construct a unique sequential algorithm which computes a given monotone and stable function, and describing the conditions on sequential algorithms which correspond to continuity with respect to each order. We illustrate by defining may and must-testing denotational semantics for a sequential functional language with bounded and unbounded choice operators. We prove that these are computationally adequate, despite the non-continuity of the must-testing semantics of unbounded nondeterminism. In the bounded case, we prove that our continuous models are fully abstract with respect to may and must-testing by identifying a simple universal type, which may also form the basis for models of the untyped lambda-calculus. In the unbounded case we observe that our model contains computable functions which are not denoted by terms, by identifying a further "weak continuity" property of the definable elements, and use this to establish that it is not fully abstract

Abstraction in directed model checking

Abstraction is one of the most important issues to cope with large and infinite state spaces in model checking and to reduce the verification efforts. The abstract system is smaller than the original one and if the abstract system satisfies a correctness specification, so does the concrete one. However, abstractions may introduce a behavior violating the specification that is not present in the original system. This paper bypasses this problem by proposing the combination of abstraction with heuristic search to improve error detection. The abstract system is explored in order to create a database that stores the exact distances from abstract states to the set of abstract error states. To check, whether or not the abstract behavior is present in the original system, effcient exploration algorithms exploit the database as a guidance

A Formal Framework for Concrete Reputation Systems

In a reputation-based trust-management system, agents maintain information about the past behaviour of other agents. This information is used to guide future trust-based decisions about interaction. However, while trust management is a component in security decision-making, many existing reputation-based trust-management systems provide no formal security-guarantees. In this extended abstract, we describe a mathematical framework for a class of simple reputation-based systems. In these systems, decisions about interaction are taken based on policies that are exact requirements on agents’ past histories. We present a basic declarative language, based on pure-past linear temporal logic, intended for writing simple policies. While the basic language is reasonably expressive (encoding e.g. Chinese Wall policies) we show how one can extend it with quantification and parameterized events. This allows us to encode other policies known from the literature, e.g., ‘one-out-of-k’. The problem of checking a history with respect to a policy is efficient for the basic language, and tractable for the quantified language when policies do not have too many variables

Stochastic Shortest Path with Energy Constraints in POMDPs

We consider partially observable Markov decision processes (POMDPs) with a set of target states and positive integer costs associated with every transition. The traditional optimization objective (stochastic shortest path) asks to minimize the expected total cost until the target set is reached. We extend the traditional framework of POMDPs to model energy consumption, which represents a hard constraint. The energy levels may increase and decrease with transitions, and the hard constraint requires that the energy level must remain positive in all steps till the target is reached. First, we present a novel algorithm for solving POMDPs with energy levels, developing on existing POMDP solvers and using RTDP as its main method. Our second contribution is related to policy representation. For larger POMDP instances the policies computed by existing solvers are too large to be understandable. We present an automated procedure based on machine learning techniques that automatically extracts important decisions of the policy allowing us to compute succinct human readable policies. Finally, we show experimentally that our algorithm performs well and computes succinct policies on a number of POMDP instances from the literature that were naturally enhanced with energy levels.Comment: Technical report accompanying a paper published in proceedings of AAMAS 201