Algorithms and Conditional Lower Bounds for Planning Problems

We consider planning problems for graphs, Markov decision processes (MDPs), and games on graphs. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an adversarial environment. We consider two planning problems where there are k different target sets, and the problems are as follows: (a) the coverage problem asks whether there is a plan for each individual target set, and (b) the sequential target reachability problem asks whether the targets can be reached in sequence. For the coverage problem, we present a linear-time algorithm for graphs and quadratic conditional lower bound for MDPs and games on graphs. For the sequential target problem, we present a linear-time algorithm for graphs, a sub-quadratic algorithm for MDPs, and a quadratic conditional lower bound for games on graphs. Our results with conditional lower bounds establish (i) model-separation results showing that for the coverage problem MDPs and games on graphs are harder than graphs and for the sequential reachability problem games on graphs are harder than MDPs and graphs; (ii) objective-separation results showing that for MDPs the coverage problem is harder than the sequential target problem.Comment: Accepted at ICAPS'1

Language-Emptiness Checking of Alternating Tree Automata Using Symbolic Reachability Analysis

AbstractAlternating tree automata and AND/OR graphs provide elegant formalisms that enable branching- time logics to be verified in linear time. The seminal work of Kupferman et al. [Orna Kupferman, Moshe Y. Vardi, and Pierre Wolper. An automata-theoretic approach to branching-time model checking. J. ACM, 47(2):312–360, 2000] showed that 1) branching-time model checking is reducible to the language non-emptiness checking of the product of two alternating automata representing the model and property under verification, and 2) the non-emptiness problem can be solved by performing a search on an AND/OR graph representing this product. Their algorithm, however, can only be implemented in an explicit-state model checker because it needs stacks to detect accept and reject runs. In this paper, we propose a BDD-based approach to check the language non-emptiness of the product automaton. We use a technique called “state recording” from Schuppan and Biere [Viktor Schuppan and Armin Biere. Efficient reduction of finite state model checking to reachability analysis. Int. Journal on Software Tools for Technology Transfer (STTT), 5(2–3):185–204, 2004] to emulate the stack mechanism from explicit-state model checking. This technique allows us to transform the product automaton into a well-defined AND/OR graph. We develop a BDD-based reachability algorithm to efficiently determine whether a solution graph for the AND/OR graph exists and thereby solve the model-checking problem. While “state recording” increases the size of the state space, the advantage of our approach lies in the memory saving BDDs can offer and the potential it opens up for optimisation of the reachability analysis. We remark that this technique always detects the shortest counter-example

Survey on assembly sequencing: a combinatorial and geometrical perspective

A systematic overview on the subject of assembly sequencing is presented. Sequencing lies at the core of assembly planning, and variants include finding a feasible sequence—respecting the precedence constraints between the assembly operations—, or determining an optimal one according to one or several operational criteria. The different ways of representing the space of feasible assembly sequences are described, as well as the search and optimization algorithms that can be used. Geometry plays a fundamental role in devising the precedence constraints between assembly operations, and this is the subject of the second part of the survey, which treats also motion in contact in the context of the actual performance of assembly operations.Peer ReviewedPostprint (author’s final draft

IST Austria Technical Report

Computing the winning set for Büchi objectives in alternating games on graphs is a central problem in computer aided verification with a large number of applications. The long standing best known upper bound for solving the problem is ̃O(n·m), where n is the number of vertices and m is the number of edges in the graph. We are the first to break the ̃O(n·m) boundary by presenting a new technique that reduces the running time to O(n2). This bound also leads to O(n2) time algorithms for computing the set of almost-sure winning vertices for Büchi objectives (1) in alternating games with probabilistic transitions (improving an earlier bound of O(n·m)), (2) in concurrent graph games with constant actions (improving an earlier bound of O(n3)), and (3) in Markov decision processes (improving for m > n4/3 an earlier bound of O(min(m1.5, m·n2/3)). We also show that the same technique can be used to compute the maximal end-component decomposition of a graph in time O(n2), which is an improvement over earlier bounds for m > n4/3. Finally, we show how to maintain the winning set for Büchi objectives in alternating games under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per operation. This is the first dynamic algorithm for this problem

Heuristic search for equivalence checking

Equivalence checking plays a crucial role in formal verification since it is a natural relation for expressing the matching of a system implementation against its specification. In this paper, we present an efficient procedure, based on heuristic search, for checking well-known bisimulation equivalences for concurrent systems specified through process algebras. The method tries to improve, with respect to other solutions, both the memory occupation and the time required for proving the equivalence of systems. A prototype has been developed to evaluate the approach on several examples of concurrent system specifications

Intelligent Business Process Optimization for the Service Industry

The company's sustainable competitive advantage derives from its capacity to create value for customers and to adapt the operational practices to changing situations. Business processes are the heart of each company. Therefore process excellence has become a key issue. This book introduces a novel approach focusing on the autonomous optimization of business processes by applying sophisticated machine learning techniques such as Relational Reinforcement Learning and Particle Swarm Optimization

Intelligent Business Process Optimization for the Service Industry

The company\u27s sustainable competitive advantage derives from its capacity to create value for customers and to adapt the operational practices to changing situations. Business processes are the heart of each company. Therefore process excellence has become a key issue. This book introduces a novel approach focusing on the autonomous optimization of business processes by applying sophisticated machine learning techniques such as Relational Reinforcement Learning and Particle Swarm Optimization

System fault diagnosis using fault tree analysis

Fault tree analysis is a method that describes all possible causes of a specified system state in terms of the state of the components within the system. Fault trees are commonly developed to analyse the adequacy of systems, from a reliability or safety point of view during the stages of design. The aim of the research presented in this thesis was to develop a method for diagnosing faults in systems using a model-based fault tree analysis approach, taking into consideration the potential for use on aircraft systems. Initial investigations have been conducted by developing four schemes that use coherent and non-coherent fault trees, the concepts of which are illustrated by applying the techniques to a simple system. These were used to consider aspects of system performance for each scheme at specified points in time. The results obtained were analysed and a critical appraisal of the findings carried out to determine the individual effectiveness of each scheme. A number of issues were highlighted from the first part of research, including the need to consider dynamics of the system to improve the method. The most effective scheme from the initial investigations was extended to take into account system dynamics through the development of a pattern recognition technique. Transient effects, including time history of flows and rate of change of fluid level were considered. The established method was then applied to a theoretical version of the BAE Systems fuel rig to investigate how the method could be utilised on a larger system. The fault detection was adapted to work with an increased number of fuel tanks and other components adding to the system complexity. The implications of expanding the method to larger systems such as a full aircraft fuel system were identified for the Nimrod MRA4