An average-case depth hierarchy theorem for Boolean circuits

We prove an average-case depth hierarchy theorem for Boolean circuits over the standard basis of $\mathsf{AND}$, $\mathsf{OR}$, and $\mathsf{NOT}$ gates. Our hierarchy theorem says that for every $d \geq 2$, there is an explicit $n$-variable Boolean function $f$, computed by a linear-size depth-$d$ formula, which is such that any depth-$(d-1)$ circuit that agrees with $f$ on $(1/2 + o_n(1))$ fraction of all inputs must have size $\exp({n^{\Omega(1/d)}}).$ This answers an open question posed by H{\aa}stad in his Ph.D. thesis. Our average-case depth hierarchy theorem implies that the polynomial hierarchy is infinite relative to a random oracle with probability 1, confirming a conjecture of H{\aa}stad, Cai, and Babai. We also use our result to show that there is no "approximate converse" to the results of Linial, Mansour, Nisan and Boppana on the total influence of small-depth circuits, thus answering a question posed by O'Donnell, Kalai, and Hatami. A key ingredient in our proof is a notion of \emph{random projections} which generalize random restrictions

Using Inhabitation in Bounded Combinatory Logic with Intersection Types for Composition Synthesis

We describe ongoing work on a framework for automatic composition synthesis from a repository of software components. This work is based on combinatory logic with intersection types. The idea is that components are modeled as typed combinators, and an algorithm for inhabitation {\textemdash} is there a combinatory term e with type tau relative to an environment Gamma? {\textemdash} can be used to synthesize compositions. Here, Gamma represents the repository in the form of typed combinators, tau specifies the synthesis goal, and e is the synthesized program. We illustrate our approach by examples, including an application to synthesis from GUI-components.Comment: In Proceedings ITRS 2012, arXiv:1307.784

The Power of Proofs: New Algorithms for Timed Automata Model Checking (with Appendix)

This paper presents the first model-checking algorithm for an expressive modal mu-calculus over timed automata, $L^{\mathit{rel}, \mathit{af}}_{\nu,\mu}$, and reports performance results for an implementation. This mu-calculus contains extended time-modality operators and can express all of TCTL. Our algorithmic approach uses an "on-the-fly" strategy based on proof search as a means of ensuring high performance for both positive and negative answers to model-checking questions. In particular, a set of proof rules for solving model-checking problems are given and proved sound and complete; we encode our algorithm in these proof rules and model-check a property by constructing a proof (or showing none exists) using these rules. One noteworthy aspect of our technique is that we show that verification performance can be improved with \emph{derived rules}, whose correctness can be inferred from the more primitive rules on which they are based. In this paper, we give the basic proof rules underlying our method, describe derived proof rules to improve performance, and compare our implementation of this model checker to the UPPAAL tool.Comment: This is the preprint of the FORMATS 2014 paper, but this is the full version, containing the Appendix. The final publication is published from Springer, and is available at http://link.springer.com/chapter/10.1007%2F978-3-319-10512-3_9 on the Springer webpag

Evidentiality in Dena'ina Athabaskan

Dena'ina evidentials are enclitics with a complex paradigmatic morphology. Their first component varies with person, while the second com- ponent varies with animacy and number, thus marking source and nature of knowledge. Although evidentiality in Dena'ina is not coded as an obligatory inflectional category on the verb, it is also not scattered throughout the gram- mar. The existence of an incipient inflectional evidential system demonstrates the ability of Athabaskan languages to innovate morphological structures outside the verb. The uniqueness of the Dena'ina system demonstrates the heterogeneity of Athabaskan grammar beyond the verb word

Finite-Degree Predicates and Two-Variable First-Order Logic

We consider two-variable first-order logic on finite words with a fixed number of quantifier alternations. We show that all languages with a neutral letter definable using the order and finite-degree predicates are also definable with the order predicate only. From this result we derive the separation of the alternation hierarchy of two-variable logic on this signature

Test of preemptive real-time systems

Time Petri nets with stopwatches not only model system/environment interactions and time constraints. They further enable modeling of suspend/resume operations in real-time systems. Assuming the modelled systems are non deterministic and partially observable, the paper proposes a test generation approach which implements an online testing policy and outputs test results that are valid for the (part of the) selected environment. A relativized conformance relation named rswtioco is defined and a test generation algorithm is presented. The proposed approach is illustrated on an example