Arbitrary Recursion Research Articles

Ray Accelerator: Efficient and Flexible Ray Tracing on a Heterogeneous Architecture

AbstractWe present a hybrid ray tracing system, where the work is divided between the CPU cores and the GPU in an integrated chip, and communication occurs via shared memory. Rays are organized in large packets that can be distributed among the two units as needed. Testing visibility between rays and the scene is mostly performed using an optimized kernel on the GPU, but the CPU can help as necessary. The CPU cores typically handle most or all shading, which makes it easy to support complex appearances. For efficiency, the CPU cores shade whole batches of rays by sorting them on material and shading each material using a vectorized kernel. In addition, we introduce a method to support light paths with arbitrary recursion, such as multiple recursive Whitted‐style ray tracing and adaptive sampling where the result of a ray is examined before sending the next, while still batching up rays for the benefit of GPU‐accelerated traversal and vectorized shading. This allows our system to achieve high rendering performance while maintaining the flexibility to accommodate different rendering algorithms.

Tight Bounds for HTN Planning

Although HTN planning is in general undecidable, there are many syntactically identifiable sub-classes of HTN problems that can be decided. For these sub-classes, the decision procedures provide upper complexity bounds. Lower bounds were often not investigated in more detail, however. We generalize a propositional HTN formalization to one that is based upon a function-free first-order logic and provide tight upper and lower complexity results along three axes: whether variables are allowed in operator and method schemas, whether the initial task and methods must be totally ordered, and where recursion is allowed (arbitrary recursion, tail-recursion, and acyclic problems). Our findings have practical implications, both for the reuse of classical planning techniques for HTN planning, and for the design of efficient HTN algorithms.

Secure distributed programming with value-dependent types

AbstractDistributed applications are difficult to program reliably and securely. Dependently typed functional languages promise to prevent broad classes of errors and vulnerabilities, and to enable program verification to proceed side-by-side with development. However, as recursion, effects, and rich libraries are added, using types to reason about programs, specifications, and proofs becomes challenging. We present F*, a full-fledged design and implementation of a new dependently typed language for secure distributed programming. Our language provides arbitrary recursion while maintaining a logically consistent core; it enables modular reasoning about state and other effects using affine types; and it supports proofs of refinement properties using a mixture of cryptographic evidence and logical proof terms. The key mechanism is a new kind system that tracks several sub-languages within F* and controls their interaction. F* subsumes two previous languages, F7 and Fine. We prove type soundness (with proofs mechanized in Coq) and logical consistency for F*. We have implemented a compiler that translates F* to .NET bytecode, based on a prototype for Fine. F* provides access to libraries for concurrency, networking, cryptography, and interoperability with C#, F#, and the other .NET languages. The compiler produces verifiable binaries with 60% code size overhead for proofs and types, as much as a 45x improvement over the Fine compiler, while still enabling efficient bytecode verification. We have programmed and verified nearly 50,000 lines of F* including new schemes for multi-party sessions; a zero-knowledge privacy-preserving payment protocol; a provenance-aware curated database; a suite of web-browser extensions verified for authorization properties; a cloud-hosted multi-tier web application with a verified reference monitor; the core F* typechecker itself; and programs translated to F* from other languages such as F7 and JavaScript.

Secure distributed programming with value-dependent types

Distributed applications are difficult to program reliably and securely. Dependently typed functional languages promise to prevent broad classes of errors and vulnerabilities, and to enable program verification to proceed side-by-side with development. However, as recursion, effects, and rich libraries are added, using types to reason about programs, specifications, and proofs becomes challenging. We present F*, a full-fledged design and implementation of a new dependently typed language for secure distributed programming. Unlike prior languages, F* provides arbitrary recursion while maintaining a logically consistent core; it enables modular reasoning about state and other effects using affine types; and it supports proofs of refinement properties using a mixture of cryptographic evidence and logical proof terms. The key mechanism is a new kind system that tracks several sub-languages within F* and controls their interaction. F* subsumes two previous languages, F7 and Fine. We prove type soundness (with proofs mechanized in Coq) and logical consistency for F*. We have implemented a compiler that translates F* to .NET bytecode, based on a prototype for Fine. F* provides access to libraries for concurrency, networking, cryptography, and interoperability with C#, F#, and the other .NET languages. The compiler produces verifiable binaries with 60% code size overhead for proofs and types, as much as a 45x improvement over the Fine compiler, while still enabling efficient bytecode verification. To date, we have programmed and verified more than 20,000 lines of F* including (1) new schemes for multi-party sessions; (2) a zero-knowledge privacy-preserving payment protocol; (3) a provenance-aware curated database; (4) a suite of 17 web-browser extensions verified for authorization properties; and (5) a cloud-hosted multi-tier web application with a verified reference monitor.

A Finite Semantics of Simply-Typed Lambda Terms for Infinite Runs of Automata

Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type hierarchy upon this interpretation of the base type gives a finite semantics for simply-typed lambda-trees. A calculus based on this semantics is proven sound and complete. In particular, for regular infinite lambda-trees it is decidable whether a given automaton has a run or not. As regular lambda-trees are precisely recursion schemes, this decidability result holds for arbitrary recursion schemes of arbitrary level, without any syntactical restriction.