TY - JOUR
AB - Given an absolutely irreducible ternary form F, the purpose of this paper is to produce better upper bounds for the number of integer solutions to the equation F=0, that are restricted to lie in very lopsided boxes. As an application of the main result, a new paucity estimate is obtained for equal sums of two like powers.
AU - Timothy Browning
AU - Heath-Brown, Roger
ID - 214
IS - 2
JF - Mathematische Zeitschrift
TI - Plane curves in boxes and equal sums of two powers
VL - 251
ER -
TY - JOUR
AB - We show that the number of nontrivial rational points of height at most B, which lie on the cubic surface x1 x2 x3 = x4 (x1 + x2 + x3)2, has order of magnitude B (log B)6. This agrees with Manin's conjecture.
AU - Timothy Browning
ID - 217
IS - 2
JF - Journal of Number Theory
TI - The density of rational points on a certain singular cubic surface
VL - 119
ER -
TY - CONF
AB - Surveying results from [5] and [6], we motivate and introduce the theory behind formalizing rich interfaces for software and hardware components. Rich interfaces specify the protocol aspects of component interaction. Their formalization, called interface automata, permits a compiler to check the compatibility of component interaction protocols. Interface automata support incremental design and independent implementability. Incremental design means that the compatibility checking of interfaces can proceed for partial system descriptions, without knowing the interfaces of all components. Independent implementability means that compatible interfaces can be refined separately, while still maintaining compatibility.
AU - de Alfaro, Luca
AU - Thomas Henzinger
ID - 4624
TI - Interface-based design
VL - 195
ER -
TY - JOUR
AB - Temporal logic is two-valued: formulas are interpreted as either true or false. When applied to the analysis of stochastic systems, or systems with imprecise formal models, temporal logic is therefore fragile: even small changes in the model can lead to opposite truth values for a specification. We present a generalization of the branching-time logic CTL which achieves robustness with respect to model perturbations by giving a quantitative interpretation to predicates and logical operators, and by discounting the importance of events according to how late they occur. In every state, the value of a formula is a real number in the interval [0,1], where 1 corresponds to truth and 0 to falsehood. The boolean operators and and or are replaced by min and max, the path quantifiers ∃ and ∀ determine sup and inf over all paths from a given state, and the temporal operators ⋄ and □ specify sup and inf over a given path; a new operator averages all values along a path. Furthermore, all path operators are discounted by a parameter that can be chosen to give more weight to states that are closer to the beginning of the path.
We interpret the resulting logic DCTL over transition systems, Markov chains, and Markov decision processes. We present two semantics for DCTL: a path semantics, inspired by the standard interpretation of state and path formulas in CTL, and a fixpoint semantics, inspired by the μ-calculus evaluation of CTL formulas. We show that, while these semantics coincide for CTL, they differ for DCTL, and we provide model-checking algorithms for both semantics.
AU - de Alfaro, Luca
AU - Faella, Marco
AU - Thomas Henzinger
AU - Majumdar, Ritankar S
AU - Stoelinga, Mariëlle
ID - 4625
IS - 1
JF - Theoretical Computer Science
TI - Model checking discounted temporal properties
VL - 345
ER -
TY - CONF
AB - We present the first demonstration of Jozsa's "counterfactual computation", using an optical Grover's search algorithm. We put the algorithm in a superposition of 'running' and 'not-running', obtaining information even though the algorithm does not run.
AU - Onur Hosten
AU - Rakher, Matthew T
AU - Barreiro, Julio T
AU - Peters, Nicholas A
AU - Kwiat, Paul G
ID - 575
TI - Counterfactual quantum computation
VL - 1
ER -