We present an automatic method which combines logical proof search and rippling heuristics to prove specifications. The key idea is to instantiate meta-variables in the proof with a simultaneous match based on rippling/reverse rippling heuristic. Underlying our rippling strategy is the rippling distance strategy which introduces a new powerful approach to rippling, as it avoids termination prob...

Using density functional theory calculations, we compute the edge energies and stresses for edges of SiC and BN nanoribbons, and the boundary energies and stresses for domain boundaries of graphene-BN superlattices. SiC and BN armchair nanoribbons show pronounced edge relaxations, which obliterate the threefold oscillatory behavior of the edge stress reported for graphene. Our calculations show...

We compare rippling and exhaustive rewriting using recursive path ordering, on a range of inductive proofs. We present statistics on success rates, branching rates and CPU times. We use these statistics to argue that rippling succeeds more often. However, these statistics also show that rippling and reduction are roughly the same in terms of average branching rate and that rippling often takes ...

Objective The widespread use of carbon nanotube-fabricated electromechanical systems has resulted in new operating scenarios for these structures, such as the presence an external magnetic field. Also, rippling can significantly impact performance nanotube-based actuators. These critical phenomena, however, are frequently overlooked theoretical beam models. This paper simulates electromagnetic ...

We describe rippling: a tactic for the heuristic control of the key part of proofs by mathematical induction. This tactic signiicantly reduces the search for a proof of a wide variety of inductive theorems. We rst present a basic version of rippling, followed by various extensions which are necessary to capture larger classes of inductive proofs. Finally, we present a general-ised form of rippl...

A power rippling method was proposed in this study to improve the cut edge quality by disturbing the natural frequency of the periodic striations in high power CO2 laser cutting. A pilot study was also designed and set up to examine the power responsibility of the laser system, which is externally controlled by a modulated analogue signal from a signal generator. Several aspects were examined i...

We propose a new version of rippling, called relational rippling. Rippling is a heuristic for guiding proof search, especially in the step cases of inductive proofs. Relational rippling is designed for representations in which value passing is by shared existential variables, as op­ posed to function nesting. Thus relational rip­ pling can be used to guide reasoning about logic programs or circ...

We present an account of rippling with proof critics suitable for use in higher order logic in Isabelle/IsaPlanner. We treat issues not previously examined, in particular regarding the existence of multiple annotations during rippling. This results in an efficient mechanism for rippling that can conjecture and prove needed lemmas automatically as well as present the resulting proof plans as Isa...

Rippling is a special type of rewriting which uses annotations to guide the derivation towards a particular goal. It has many desirable properties. For example, it terminates yet allows rules like associativity to be used in both directions; it is also highly goal-directed applying only those rewrite rules needed to remove the diierences between the goal and some hypothesis. Although it has bee...