There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

ing WS1S Systems to Verify Parameterized Networks . . . . . . . . . . . . 188 Kai Baukus, Saddek Bensalem, Yassine Lakhnech and Karsten Stahl FMona: A Tool for Expressing Validation Techniques over Infinite State Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 J.-P. Bodeveix and M. Filali Transitive Closures of Regular Relations for Verifying Infinite-State Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 Bengt Jonsson and Marcus Nilsson Diagnostic and Test Generation Using Static Analysis to Improve Automatic Test Generation . . . . . . . . . . . . . 235 Marius Bozga, Jean-Claude Fernandez and Lucian Ghirvu Efficient Diagnostic Generation for Boolean Equation Systems . . . . . . . . . . . . 251 Radu Mateescu Efficient Model-Checking Compositional State Space Generation with Partial Order Reductions for Asynchronous Communicating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 Jean-Pierre Krimm and Laurent Mounier Checking for CFFD-Preorder with Tester Processes . . . . . . . . . . . . . . . . . . . . . . . 283 Juhana Helovuo and Antti Valmari Fair Bisimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Thomas A. Henzinger and Sriram K. Rajamani Integrating Low Level Symmetries into Reachability Analysis . . . . . . . . . . . . . 315 Karsten Schmidt Model-Checking Tools Model Checking Support for the ASM High-Level Language . . . . . . . . . . . . . . 331 Giuseppe Del Castillo and Kirsten Winter Table of

Tools and Algorithms for the Construction and Analysis of Systems. Proc. TACAS 2009

http://user.it.uu.se/~jarst116/slides/week4.pdf

Graph-Based Algorithms for Boolean Function Manipulation

We consider a fully SAT-based method of unbounded symbolic model checking based on computing Craig interpolants. In benchmark studies using a set of large industrial circuit verification instances, this method is greatly more efficient than BDD-based symbolic model checking, and compares favorably to some recent SAT-based model checking methods on positive instances.

Interpolation and SAT-based model checking

Conflict-based Search (CBS) is a effective approach to optimal multi-agent path finding. However, performance of CBS approaches degrade rapidly in highly-contended graphs with many agents. One of the reasons this occurs is that CBS does not detect independent subproblems; i.e. it can re-solve the same conflicts between the same pairs of agents up to exponentially many times, each time along a different branch. Constraint programming approaches with nogood learning avoid this kind of duplication of effort by storing nogoods that record the reasons for conflicts. This can exponentially reduce search in constraint programming. In this work, we present Lazy CBS, a new approach to multi-agent pathfinding which replaces the high-level solver of CBS with a lazily constructed constraint programming model with nogoods. We use core-guided depth-first search to explore the space of conflicts and we detect along each branch reusable nogoods which help to quickly identify feasible solutions. Our experiments show that Lazy CBS can significantly improve on the state-of-the-art for optimal MAPF problems under the sumof-costs metric, especially in cases where there exists significant contention.

/pdf/lazy-cbs-implicit-conflict-based-search-using-lazy-clause-3xnhfcgs00.pdf

Lazy CBS: Implicit Conflict-Based Search Using Lazy Clause Generation

Data analytics plays a significant role in gaining insight of big data that can benefit in decision making and problem solving for various application domains such as science, engineering, and commerce. Cloud computing is a suitable platform for Big Data Analytic Applications (BDAAs) that can greatly reduce application cost by elastically provisioning resources based on user requirements and in a pay as you go model. BDAAs are typically catered for specific domains and are usually expensive. Moreover, it is difficult to provision resources for BDAAs with fluctuating resource requirements and reduce the resource cost. As a result, BDAAs are mostly used by large enterprises. Therefore, it is necessary to have a general Analytics as a Service (AaaS) platform that can provision BDAAs to users in various domains as consumable services in an easy to use way and at lower price. To support the AaaS platform, our research focuses on efficiently scheduling Cloud resources for BDAAs to satisfy Quality of Service (QoS) requirements of budget and deadline for data analytic requests and maximize profit for the AaaS platform. We propose an admission control and resource scheduling algorithm, which not only satisfies QoS requirements of requests as guaranteed in Service Level Agreements (SLAs), but also increases the profit for AaaS providers by offering a cost-effective resource scheduling solution. We propose the architecture and models for the AaaS platform and conduct experiments to evaluate the proposed algorithm. Results show the efficiency of the algorithm in SLA guarantee, profit enhancement, and cost saving.

SLA-Based Resource Scheduling for Big Data Analytics as a Service in Cloud Computing Environments

We consider two new types of pairwise path symmetries which appear in the context of Multi-Agent Path Finding (MAPF). The first of them, corridor symmetry, arises when two agents attempt to pass through the same narrow passage but in opposite directions. The second, target symmetry, arises when the shortest path of one agent requires the target location of a second agent after the second agent has already arrived. These symmetries can produce an exponential blowup in the space of possible collision resolutions, leading to timeout failure even for state-of-the-art algorithms such as Conflict-Based Search. We propose to break symmetries using new reasoning techniques that: (1) detect each type of situation and, (2) resolve them by introducing specialized constraints. We implement our ideas in the context of Conflict-Based Search where, in a range of experiments, we report up to an order-of-magnitude improvement in runtime performance and, in some cases, more than a doubling in success rate.

New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding.

Pairwise symmetry reasoning for multi-agent path finding search

Multi-valued decision diagrams (MDDs) are a convenient approach to representing many kinds of constraints including table constraints, regular constraints, complex set and multiset constraints, as well as ad-hoc problem specific constraints. This paper introduces an incremental propagation algorithm for MDDs, and explores several methods for incorporating explanations with MDD-based propagators. We demonstrate that these techniques can provide significantly improved performance when solving a variety of problems.

/pdf/mdd-propagators-with-explanation-3bf02y55va.pdf

Graeme Gange

Papers

Lazy CBS: Implicit Conflict-Based Search Using Lazy Clause Generation

SLA-Based Resource Scheduling for Big Data Analytics as a Service in Cloud Computing Environments

New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding.

Pairwise symmetry reasoning for multi-agent path finding search

MDD propagators with explanation