A linear time algorithm for the orbit problem over cyclic groups

The orbit problem is at the heart of symmetry reduction methods for model checking concurrent systems. It asks whether two given configurations in a concurrent system (represented as finite strings over some finite alphabet) are in the same orbit with respect to a given finite permutation group (represented by their generators) acting on this set of configurations by permuting indices. It is known that the problem is in general as hard as the graph isomorphism problem, whose precise complexity (whether it is solvable in polynomial-time) is a long-standing open problem. In this paper, we consider the restriction of the orbit problem when the permutation group is cyclic (i.e. generated by a single permutation), an important restriction of the problem. It is known that this subproblem is solvable in polynomial-time. Our main result is a linear-time algorithm for this subproblem.Comment: Accepted in Acta Informatica in Nov 201

The Symmetry Method for Coloured Petri Nets

This booklet is the author's PhD-dissertation

Improving Model-Based Software Synthesis: A Focus on Mathematical Structures

Computer hardware keeps increasing in complexity. Software design needs to keep up with this. The right models and abstractions empower developers to leverage the novelties of modern hardware. This thesis deals primarily with Models of Computation, as a basis for software design, in a family of methods called software synthesis. We focus on Kahn Process Networks and dataflow applications as abstractions, both for programming and for deriving an efficient execution on heterogeneous multicores. The latter we accomplish by exploring the design space of possible mappings of computation and data to hardware resources. Mapping algorithms are not at the center of this thesis, however. Instead, we examine the mathematical structure of the mapping space, leveraging its inherent symmetries or geometric properties to improve mapping methods in general. This thesis thoroughly explores the process of model-based design, aiming to go beyond the more established software synthesis on dataflow applications. We starting with the problem of assessing these methods through benchmarking, and go on to formally examine the general goals of benchmarks. In this context, we also consider the role modern machine learning methods play in benchmarking. We explore different established semantics, stretching the limits of Kahn Process Networks. We also discuss novel models, like Reactors, which are designed to be a deterministic, adaptive model with time as a first-class citizen. By investigating abstractions and transformations in the Ohua language for implicit dataflow programming, we also focus on programmability. The focus of the thesis is in the models and methods, but we evaluate them in diverse use-cases, generally centered around Cyber-Physical Systems. These include the 5G telecommunication standard, automotive and signal processing domains. We even go beyond embedded systems and discuss use-cases in GPU programming and microservice-based architectures

Replication and Abstraction: Symmetry in Automated Formal Verification.

This article surveys fundamental and applied aspects of symmetry in system models, and of symmetry reduction methods used to counter state explosion in model checking, an automated formal verification technique. While covering the research field broadly, we particularly emphasize recent progress in applying the technique to realistic systems, including tools that promise to elevate the scope of symmetry reduction to large-scale program verification. The article targets researchers and engineers interested in formal verification of concurrent systems

Enhancing State Space Reduction Methods for Model Checking

Ph.DDOCTOR OF PHILOSOPH

On the constructive orbit problem

Symmetry reduction techniques aim to combat the state-space explosion problem for model checking by restricting search to representative states from equivalence classes with respect to a group of symmetries. The standard approach to representative computation involves converting a state to its minimal image under a permutation group G, before storing the state. This is known as the Constructive orbit problem (COP), and is NP hard. It may be possible to solve the COP efficiently if G is known to have certain structural properties: in particular if G is isomorphic to a full symmetry group, or G is a disjoint/wreath product of subgroups. We extend existing results on solving the COP efficiently for fully symmetric groups, and investigate the problem of automatically classifying an arbitrary permutation group as a disjoint/wreath product of subgroups. We also present an approximate COP strategy based on local search, and some computational group-theoretic optimisations to improve the basic approach of solving the COP by symmetry group enumeration. Experimental results using the \topspin\ symmetry reduction package, which interfaces with the computational group-theoretic system GAP, illustrate the effectiveness of our techniques