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Full-Text Articles in Physical Sciences and Mathematics
Shortest Path Based Decision Making Using Probabilistic Inference, Akshat Kumar
Shortest Path Based Decision Making Using Probabilistic Inference, Akshat Kumar
Research Collection School Of Computing and Information Systems
We present a new perspective on the classical shortest path routing (SPR) problem in graphs. We show that the SPR problem can be recast to that of probabilistic inference in a mixture of simple Bayesian networks. Maximizing the likelihood in this mixture becomes equivalent to solving the SPR problem. We develop the well known Expectation-Maximization (EM) algorithm for the SPR problem that maximizes the likelihood, and show that it does not get stuck in a locally optimal solution. Using the same probabilistic framework, we then address an NP-Hard network design problem where the goal is to repair a network of …
Verifying Monadic Second-Order Properties Of Graph Programs, Christopher M. Poskitt, Detlef Plump
Verifying Monadic Second-Order Properties Of Graph Programs, Christopher M. Poskitt, Detlef Plump
Research Collection School Of Computing and Information Systems
The core challenge in a Hoare- or Dijkstra-style proof system for graph programs is in defining a weakest liberal precondition construction with respect to a rule and a postcondition. Previous work addressing this has focused on assertion languages for first-order properties, which are unable to express important global properties of graphs such as acyclicity, connectedness, or existence of paths. In this paper, we extend the nested graph conditions of Habel, Pennemann, and Rensink to make them equivalently expressive to monadic second-order logic on graphs. We present a weakest liberal precondition construction for these assertions, and demonstrate its use in verifying …
Verifying Total Correctness Of Graph Programs, Christopher M. Poskitt, Detlef Plump
Verifying Total Correctness Of Graph Programs, Christopher M. Poskitt, Detlef Plump
Research Collection School Of Computing and Information Systems
GP 2 is an experimental nondeterministic programming language based on graph transformation rules, allowing for visual programming and the solving of graph problems at a high-level of abstraction. In previous work we demonstrated how to verify graph programs using a Hoare-style proof calculus, but only partial correctness was considered. In this paper, we add new proof rules and termination functions, which allow for proofs to additionally guarantee that program executions always terminate (weak total correctness), or that programs always terminate and do so without failure (total correctness). We show that the new proof rules are sound with respect to the …
Verification Of Graph Programs, Christopher M. Poskitt
Verification Of Graph Programs, Christopher M. Poskitt
Research Collection School Of Computing and Information Systems
GP (for Graph Programs) is an experimental nondeterministic programming language which allows for the manipulation of graphs at a high level of abstraction. The program states of GP are directed labelled graphs. These are manipulated directly via the application of (conditional) rule schemata, which generalise double-pushout rules with expressions over labels and relabelling. In contrast with graph grammars, the application of these rule schemata is directed by a number of simple control constructs including sequential composition, conditionals, and as-long-as-possible iteration. GP shields programmers at all times from low-level implementation issues (e.g. graph representation), and with its nondeterministic semantics, allows one …