Stephen Bloch

Delayed Binary Search, or Playing Twenty Questions with a Procrastinator

AbstractWe study the classic binary search problem, with a delay between query and answer. For all constant delays, we give matching upper and lower bounds on the number of queries.

Sharply Bounded Alternation and Quasilinear Time

Abstract. We define the sharply bounded hierarchy, SBH(QL)}, a hierarchy of classes within P , using quasilinear-time computation and quantification over strings of length log n . It generalizes the limited nondeterminism hierarchy introduced by Buss and Goldsmith, while retaining the invariance properties. The new hierarchy has several alternative characterizations. We define both SBH(QL) and its corresponding hierarchy of function classes, and present a variety of problems in these classes, including ≤qlm -complete problems for each class in SBH(QL). We discuss the structure of the hierarchy, and show that determining its precise relationship to deterministic time classes can imply P≠ PSPACE . We present characterizations of SBH(QL) relations based on alternating Turing machines and on first-order definability, as well as recursion-theoretic characterizations of function classes corresponding to SBH(QL).

On parallel hierarchies and Rki

This paper defines natural hierarchies of function and relation classes □i,kc and Δi,kc, constructed from parallel complexity classes in a manner analogous to the polynomial-time hierarchy. It is easily shown that □i−1,kp ⊆ □c,kc ⊆ □i,kp and similarly for the Δ classes. The class □i,3c coincides with the single-valued functions in Buss et al.s class F℘3Σi−1,3p[wit, logO(1)] (see [11]), and analogously for other growth rates. Furthermore, the class □i,kc comprises exactly the functions Σi,kb-definable in Ski−1, and if Tki−1 is ∀∃Σi,kb-conservative over Ski−1, then □i,kp is completely parallelizable. All functions in □i,kc are Σi,kb-definable in Rki; this suffices to show that if the known ∀∃Σi,kb conservativity between R3i and S3i−1 extends to R2i and S2i−1, then NC = NC1 relative to an oracle in PH. We prove a KPT-style witnessing theorem for Ski using constantly many rounds of □i,kc interactive computation, and thus show that if Ski ≡ Rki+1 then the bounded arithmetic hierarchy collapses, provably in Ski.

On Parallel Hierarchies and R_k^i

This paper defines natural hierarchies of function and relation classes, constructed from parallel complexity classes in a manner analogous to the polynomial-time hierarchy. A number of structural results about these classes are proven: relationships between them and the levels of PH, a Buss-style witnessing theorem relating the levels of these hierarchies to definability in the bounded arithmetic theories R k i (generalizing [1] and improving on [9]), a conservation result between S k i andR k i+k , and results analogous to those of [18, 8, 16] relating conservationbetween theories of bounded arithmetic to the collapse of complexityclasses

Program by design: from animations to data structures (abstract only)

We present the Program by Design introductory CS curriculum through the lenses of graphics, animations, algebra, and data structures. Animations programming is popular for CS1, but many such curricula lack clean paths into CS2. Program by Design is different. Using and reinforcing concepts from algebra, students learn to write animations (including standard topics such as model/view separation and event-handling), then move seamlessly into working with structured data, lists, trees, and objects. The curriculum emphasizes design, testing, and writing maintainable programs, without losing the engagement of animations. The workshop uses lectures and hands-on exercises to provide high- school and college teachers an overview of the approach. See www.programbydesign.org. Laptop Optional.

Program by design: TeachScheme/ReachJava (abstract only)

Program by Design is a new name for the comprehensive introduction to programming at all levels that began with TeachScheme/ReachJava. This unconventional introductory computing curriculum covers both functional and the object- oriented program design in a systematic design-based style, enforcing test-first design from the beginning. The Bootstrap curriculum makes programming and algebra exciting for children ages 11-15. Special libraries support the design of interactive graphics-based games, musical explorations, client-server and mobile computing. We invite you to come and meet those who have used the curriculum, learn about new additions, libraries, bring in your experiences with the curriculum, show your projects, or ask questions about how it works and how you can use it. This work is sponsored by two NSF DUE CCLI grants: Redesigning Introductory Computing: The Design Discipline, Grant #00618543, and Integrating Test Design into Computing Curriculum from the Beginning, Grant #0920182.