Implementing Groundness Analysis with Definite Boolean Functions

The domain of definite Boolean functions, Def, can be used to express the groundness of, and trace grounding dependencies between, program variables in (constraint) logic programs. In this paper, previously unexploited computational properties of Def are utilised to develop an efficient and succinct groundness analyser that can be coded in Prolog. In particular, entailment checking is used to prevent unnecessary least upper bound calculations. It is also demonstrated that join can be defined in terms of other operations, thereby eliminating code and removing the need for preprocessing formulae to a normal form. This saves space and time. Furthermore, the join can be adapted to straightforwardly implement the downward closure operator that arises in set sharing analyses. Experimental results indicate that the new Def implementation gives favourable results in comparison with BDD-based groundness analyses

Efficient Groundness Analysis in Prolog

Boolean functions can be used to express the groundness of, and trace grounding dependencies between, program variables in (constraint) logic programs. In this paper, a variety of issues pertaining to the efficient Prolog implementation of groundness analysis are investigated, focusing on the domain of definite Boolean functions, Def. The systematic design of the representation of an abstract domain is discussed in relation to its impact on the algorithmic complexity of the domain operations; the most frequently called operations should be the most lightweight. This methodology is applied to Def, resulting in a new representation, together with new algorithms for its domain operations utilising previously unexploited properties of Def -- for instance, quadratic-time entailment checking. The iteration strategy driving the analysis is also discussed and a simple, but very effective, optimisation of induced magic is described. The analysis can be implemented straightforwardly in Prolog and the use of a non-ground representation results in an efficient, scalable tool which does not require widening to be invoked, even on the largest benchmarks. An extensive experimental evaluation is givenComment: 31 pages To appear in Theory and Practice of Logic Programmin

Hennessy-Milner Logic with Greatest Fixed Points as a Complete Behavioural Specification Theory

There are two fundamentally different approaches to specifying and verifying properties of systems. The logical approach makes use of specifications given as formulae of temporal or modal logics and relies on efficient model checking algorithms; the behavioural approach exploits various equivalence or refinement checking methods, provided the specifications are given in the same formalism as implementations. In this paper we provide translations between the logical formalism of Hennessy-Milner logic with greatest fixed points and the behavioural formalism of disjunctive modal transition systems. We also introduce a new operation of quotient for the above equivalent formalisms, which is adjoint to structural composition and allows synthesis of missing specifications from partial implementations. This is a substantial generalisation of the quotient for deterministic modal transition systems defined in earlier papers

Scale-Invariant Gravity: Geometrodynamics

We present a scale-invariant theory, conformal gravity, which closely resembles the geometrodynamical formulation of general relativity (GR). While previous attempts to create scale-invariant theories of gravity have been based on Weyl's idea of a compensating field, our direct approach dispenses with this and is built by extension of the method of best matching w.r.t scaling developed in the parallel particle dynamics paper by one of the authors. In spatially-compact GR, there is an infinity of degrees of freedom that describe the shape of 3-space which interact with a single volume degree of freedom. In conformal gravity, the shape degrees of freedom remain, but the volume is no longer a dynamical variable. Further theories and formulations related to GR and conformal gravity are presented. Conformal gravity is successfully coupled to scalars and the gauge fields of nature. It should describe the solar system observations as well as GR does, but its cosmology and quantization will be completely different.Comment: 33 pages. Published version (has very minor style changes due to changes in companion paper

Formal synthesis of control and communication schemes

Thesis (Ph.D.)--Boston UniversityIn traditional motion planning, the problem is simply specified as "go from A to B while avoiding obstacles", where A and B are two configurations or regions of interest in the robot workspace. However, a large number of robotic applications require more expressive specification languages, which allow for logical and temporal statements about the satisfaction of properties of interest. Examples include "visit A and B infinitely often, always avoid C, and do not visit D unless E vas visited before". Such task specifications cannot be trivially converted to a sequence of "go from A to B" primitives. This thesis establishes theoretical and computational frameworks for automatic synthesis of robot control and communication schemes that are correct-by-construction from task specifications given in expressive languages. We consider a purely discrete scenario, in which the dynamics of each robot is modeled as a finite discrete system. The first problem addressed in this thesis is the generation of provably-correct individual control and communication strategies for a team of robots from rich task specifications in the case when the workspace is static. The second problem relaxes this assumption and considers a scenario in which the environment changes according to some unknown patterns. It proposed a combined learning and formal synthesis approach to generate correct control policies. To tackle the first problem, we draw inspirations from the research fields of formal verification and synthesis, distributed formal synthesis, and concurrency theory. We consider a team of robots that can move among the regions of a partitioned environment and have known capabilities of servicing a set of requests that can occur in the regions of the partition. Some of these requests can be serviced by a robot individually, while some require the cooperation of groups of robots. We propose a top-down approach, in which global specifications given as Regular Expressions (RE) or Linear Temporal Logics (LTL) can be decomposed into local (individual) specifications, which can then be used to automatically synthesize robot control and communication strategies. To address the second problem, we bring together automata learning methods from the field of theoretical linguistics and techniques from temporal logic games and probabilistic model checking, to develop a provably-correct control strategy for robots moving in an environment with unknown dynamics. The robots are required to achieve a surveillance mission, in which a certain request needs to be serviced repeatedly, while the expected time in between consecutive services is minimized and additional temporal logic constraints are satisfied. We define a fragment of Linear Temporal Logic (LTL) to describe such a mission. We consider a single agent case at first and then extend the results to multi-agent systems. To this end, we apply approximate dynamic programming to our computational framework, which leads to significant reduction of computational time. To demonstrate the proposed theoretical and computational frameworks, we implement the derived algorithms in two experimental platforms, the Robotic Urban-Like Environment (RULE) and the Robotic InDoor-like Environment (RIDE). We assign tasks to the team using Regular Expressions or Linear Temporal Logics over requests occurring at regions in the environment. The robots are automatically deployed to complete the missions