Efficient Reflection String Analysis via Graph Coloring

Static analyses for reflection and other dynamic language features have recently increased in number and advanced in sophistication. Most such analyses rely on a whole-program model of the flow of strings, through the stack and heap. We show that this global modeling of strings remains a major bottleneck of static analyses and propose a compact encoding, in order to battle unnecessary complexity. In our encoding, strings are maximally merged if they can never serve to differentiate class members in reflection operations. We formulate the problem as an instance of graph coloring and propose a fast polynomial-time algorithm that exploits the unique features of the setting (esp. large cliques, leading to hundreds of colors for realistic programs). The encoding is applied to two different frameworks for string-guided Java reflection analysis from past literature and leads to significant optimization (e.g., a ~2x reduction in the number of string-flow inferences), for a whole-program points-to analysis that uses strings

Span programs and quantum algorithms for st-connectivity and claw detection

We introduce a span program that decides st-connectivity, and generalize the span program to develop quantum algorithms for several graph problems. First, we give an algorithm for st-connectivity that uses O(n d^{1/2}) quantum queries to the n x n adjacency matrix to decide if vertices s and t are connected, under the promise that they either are connected by a path of length at most d, or are disconnected. We also show that if T is a path, a star with two subdivided legs, or a subdivision of a claw, its presence as a subgraph in the input graph G can be detected with O(n) quantum queries to the adjacency matrix. Under the promise that G either contains T as a subgraph or does not contain T as a minor, we give O(n)-query quantum algorithms for detecting T either a triangle or a subdivision of a star. All these algorithms can be implemented time efficiently and, except for the triangle-detection algorithm, in logarithmic space. One of the main techniques is to modify the st-connectivity span program to drop along the way "breadcrumbs," which must be retrieved before the path from s is allowed to enter t.Comment: 18 pages, 4 figure

Circular Coloring of Random Graphs: Statistical Physics Investigation

Circular coloring is a constraints satisfaction problem where colors are assigned to nodes in a graph in such a way that every pair of connected nodes has two consecutive colors (the first color being consecutive to the last). We study circular coloring of random graphs using the cavity method. We identify two very interesting properties of this problem. For sufficiently many color and sufficiently low temperature there is a spontaneous breaking of the circular symmetry between colors and a phase transition forwards a ferromagnet-like phase. Our second main result concerns 5-circular coloring of random 3-regular graphs. While this case is found colorable, we conclude that the description via one-step replica symmetry breaking is not sufficient. We observe that simulated annealing is very efficient to find proper colorings for this case. The 5-circular coloring of 3-regular random graphs thus provides a first known example of a problem where the ground state energy is known to be exactly zero yet the space of solutions probably requires a full-step replica symmetry breaking treatment.Comment: 19 pages, 8 figures, 3 table

Exponential improvement in precision for simulating sparse Hamiltonians

We provide a quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous methods. Specifically, we show that a $d$-sparse Hamiltonian $H$ acting on $n$ qubits can be simulated for time $t$ with precision $\epsilon$ using $O\big(\tau \frac{\log(\tau/\epsilon)}{\log\log(\tau/\epsilon)}\big)$ queries and $O\big(\tau \frac{\log^2(\tau/\epsilon)}{\log\log(\tau/\epsilon)}n\big)$ additional 2-qubit gates, where $\tau = d^2 \|{H}\|_{\max} t$. Unlike previous approaches based on product formulas, the query complexity is independent of the number of qubits acted on, and for time-varying Hamiltonians, the gate complexity is logarithmic in the norm of the derivative of the Hamiltonian. Our algorithm is based on a significantly improved simulation of the continuous- and fractional-query models using discrete quantum queries, showing that the former models are not much more powerful than the discrete model even for very small error. We also simplify the analysis of this conversion, avoiding the need for a complex fault correction procedure. Our simplification relies on a new form of "oblivious amplitude amplification" that can be applied even though the reflection about the input state is unavailable. Finally, we prove new lower bounds showing that our algorithms are optimal as a function of the error.Comment: v1: 27 pages; Subsumes and improves upon results in arXiv:1308.5424. v2: 28 pages, minor change

The harmonious coloring number of a graph

AbstractHopcroft and Krishnamoorthy (1983) have shown that the harmonious coloring problem is NP-complete, introducing the notion of a harmonious coloring of a graph as being a vertex coloring for which no two edges receive the same color-pair. In this report we construct efficient harmonious colorings of complete binary trees, 2 and 3-dimensional grids, and n-dimensional cubes

IIFA: Modular Inter-app Intent Information Flow Analysis of Android Applications

Android apps cooperate through message passing via intents. However, when apps do not have identical sets of privileges inter-app communication (IAC) can accidentally or maliciously be misused, e.g., to leak sensitive information contrary to users expectations. Recent research considered static program analysis to detect dangerous data leaks due to inter-component communication (ICC) or IAC, but suffers from shortcomings with respect to precision, soundness, and scalability. To solve these issues we propose a novel approach for static ICC/IAC analysis. We perform a fixed-point iteration of ICC/IAC summary information to precisely resolve intent communication with more than two apps involved. We integrate these results with information flows generated by a baseline (i.e. not considering intents) information flow analysis, and resolve if sensitive data is flowing (transitively) through components/apps in order to be ultimately leaked. Our main contribution is the first fully automatic sound and precise ICC/IAC information flow analysis that is scalable for realistic apps due to modularity, avoiding combinatorial explosion: Our approach determines communicating apps using short summaries rather than inlining intent calls, which often requires simultaneously analyzing all tuples of apps. We evaluated our tool IIFA in terms of scalability, precision, and recall. Using benchmarks we establish that precision and recall of our algorithm are considerably better than prominent state-of-the-art analyses for IAC. But foremost, applied to the 90 most popular applications from the Google Playstore, IIFA demonstrated its scalability to a large corpus of real-world apps. IIFA reports 62 problematic ICC-/IAC-related information flows via two or more apps/components

Practice Room Acoustics: What Matters to Musicians About the Practice Space

Why do people always prefer the practice room in the corner on the second floor than the others? What’s the reason why string players often go for the “dryer” room than the wind players? Wondering why brass players often occupy the resonant room? This paper is here to decipher all the mysteries behind all of the questions above by the acoustic analysis suggested by Bonnelo and the other supplying papers on sound absorbing materials. The question to be answered is how the rooms are different from each other in terms of their dimensions and damping surfaces. Eventually, construct a criteria for adjusting the acoustic characteristic by using sound absorbing materials. Through a survey filled out by conservatory students, it informs general preferences of choosing practice room and a frequency­ dependent reverberation time test is run accordingly. Having gathered all the information, it can be concluded that there is a direct relation between how preferable a room is and room dimension and the evenness of reverberation time throughout a frequency interval. Besides from the method of damping excessive resonance through locating high and low pressure area of the standing wave suggested by the Bonello paper, there are also possibilities of using different absorbing materials and Helmholtz resonator to change the reverberation time and modal density of the targeting frequency of a room. Therefore, with the results of this paper, musicians are a step closer to a simple yet career­ changing acoustic tool for constructing practice rooms