Engineering PapersSearch

SEARCH · Engineering Papers

Results for “Interactive Theorem Proving”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

25 records · Page 2

Machine-checked proofs of the design and implementation of a fault-tolerant circuit

A formally verified implementation of the 'oral messages' algorithm of Pease, Shostak, and Lamport is described. An abstract implementation of the algorithm is verified to achieve interactive consistency in the presence of faults. This abstract characterization is then mapped down to a hardware level implementation which inherits the fault-tolerant characteristics of the abstract version. All steps in the proof were checked with the Boyer-Moore theorem prover. A significant results is the demonstration of a fault-tolerant device that is formally specified and whose implementation is proved correct with respect to this specification. A significant simplifying assumption is that the redundant processors behave synchronously. A mechanically checked proof that the oral messages algorithm is 'optimal' in the sense that no algorithm which achieves agreement via similar message passing can tolerate a larger proportion of faulty processor is also described.

Bevier, William R.

Formal verification of an oral messages algorithm for interactive consistency

The formal specification and verification of an algorithm for Interactive Consistency based on the Oral Messages algorithm for Byzantine Agreement is described. We compare our treatment with that of Bevier and Young, who presented a formal specification and verification for a very similar algorithm. Unlike Bevier and Young, who observed that 'the invariant maintained in the recursive subcases of the algorithm is significantly more complicated than is suggested by the published proof' and who found its formal verification 'a fairly difficult exercise in mechanical theorem proving,' our treatment is very close to the previously published analysis of the algorithm, and our formal specification and verification are straightforward. This example illustrates how delicate choices in the formulation of the problem can have significant impact on the readability of its formal specification and on the tractability of its formal verification.

Rushby, John

QA4, a language for artificial intelligence.

Introduction of a language for problem solving and specifically robot planning, program verification, and synthesis and theorem proving. This language, called question-answerer 4 (QA4), embodies many features that have been found useful for constructing problem solvers but have to be programmed explicitly by the user of a conventional language. The most important features of QA4 are described, and examples are provided for most of the material introduced. Language features include backtracking, parallel processing, pattern matching, set manipulation, and pattern-triggered function activation. The language is most convenient for use in an interactive way and has extensive trace and edit facilities.

Derksen, J. A. C.

Formalizing Probabilistic Safety Claims

A safety claim for a system is a statement that the system, which is subject to hazardous conditions, satisfies a given set of properties. Following work by John Rushby and Bev Littlewood, this paper presents a mathematical framework that can be used to state and formally prove probabilistic safety claims. It also enables hazardous conditions, their uncertainties, and their interactions to be integrated into the safety claim. This framework provides a formal description of the probabilistic composition of an arbitrary number of hazardous conditions and their effects on system behavior. An example is given of a probabilistic safety claim for a conflict detection algorithm for aircraft in a 2D airspace. The motivation for developing this mathematical framework is that it can be used in an automated theorem prover to formally verify safety claims.

Herencia-Zapana, Heber

Cooperation Among Theorem Provers

This is a final report, which supports NASA's PECSEE (Persistent Cognizant Software Engineering Environment) effort and complements the Kestrel Institute project "Inference System Integration via Logic Morphism". The ultimate purpose of the project is to develop a superior logical inference mechanism by combining the diverse abilities of multiple cooperating theorem provers. In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's, SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The PVS system (from SRI) in only automatic within decidable theories, but it has well-designed interactive capabilities: furthermore, it includes higher-order logic, not just first-order logic. The NuPRL system from Cornell University and the STeP system from Stanford University have facilities for constructive logic and temporal logic, respectively - both are interactive. It is often suggested - for example, in the anonymous "QED Manifesto"-that we should pool the resources of all these theorem provers into a single system, so that the strengths of one can compensate for the weaknesses of others, and so that effort will not be duplicated. However, there is no straightforward way of doing this, because each system relies on its own language and logic for its success. Thus. SNARK uses ordinary first-order logic with equality, PVS uses higher-order logic. and NuPRL uses constructive logic. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages. Kestrel's SPECWARE system has been the vehicle for the implementation.

Waldinger, Richard J.

TPSAS-NF1676L-9990-DND

PVS (Prototype Veri cation System)1 is an interactive environment for the specification and verification of systems. PVS provides a strongly typed specification language, which is based on Higher-Order Logic. The type system of PVS supports: sub-typing, dependent-types, abstract data types, parametric types, records, unions, and tuples. The PVS theorem prover includes decision procedures for a variety of theories such as linear arithmetic, propositional logic, and temporal logic. This seminar will provide a gentle introduction to the basic and advanced features of PVS, including: theory interpretations, real number proving, batch proving, rapid prototyping, and strategy development. All these features are illustrated with simple examples and exercises.

César Muñoz

Disruptive Technologies and Their Putative Impacts Upon Society and Aerospace- Entering The Virtual Age

Developments in technology over the recent decades have been extraordinary. They include the IT, bio, nano, and now quantum and energetics technology arenas and their many combinatorial interactions and impacts. In the main, these are at the frontiers of the small and in a combinational, synergistic feeding frenzy with each other. They fall under the broad category of Disruptive Technologies and have greatly altered society. The outlook for the runout of these and other technology developments augers mid-term to later alterations in components of the human existence theorem, including the requirement to work for our living and our physiological makeup and longevity (Ref 1). The IT revolution began in the 1950s with the development of solid-state electronics. The biologics revolution began later in the 1960s and 1970s with DNA and genomics, and the nano revolution in the 1990s with self-forming nano systems and carbon nanotubes. Quantum technology is now developing rapidly, aided by enabling nano systems, and the energetics revolution is providing ever more efficient and less expensive renewable energy sources. The IT revolution has produced improvements of an astounding eleven orders of magnitude in computing speed since the late 1950s. As we shift from silicon to biological, optical, nano, molecular, and atomic computing, improvements of some 4 orders of magnitude are evidently possible from either optical or DNA computing [Refs 2and 3], then there are combinatorials. Then there is quantum computing, under development worldwide for an increasing number of applications and proffering phenomenal capabilities. The current fastest computers are considerably beyond human brain speed. Machine intelligence is developing well after decades of inadequate machine capability, now no longer the case, and a detour into expert systems. Researchers in machine intelligence are now pursuing deep learning approaches using neural nets, which are proving to be extremely useful. Some believe the frontier of potential human-level machine intelligence may be found in biomimetics and brain-emulation approaches. There is even a possibility of “emergence”—i.e., when the machine intelligence is complex enough that it “wakes up,” as when human intelligence emerged via evolution during the million-plus years of the hunter-gatherer epoch [ Ref 4]. In fact, some posit that human intelligence can be improved upon and is only a cul-de-sac of what is conceivable. The IT revolution has produced massive changes in human society and economics—from the Internet, enabling the rapid expansion of knowledgeability (and even what is knowable), to an increasingly pervasive trend of “tele-everything.” The extraordinary compilation, storage, and availability of truly massive amounts of information could, when combined with AI and under the mantra of “big data,” greatly improve many of our technical and commercial processes and their content including elucidating new heuristic governing laws.

Dennis M. Bushnell