21 research outputs found
Synthesis Of Distributed Protocols From Scenarios And Specifications
Distributed protocols, typically expressed as stateful agents communicating asynchronously over buffered communication channels, are difficult to design correctly. This difficulty has spurred decades of research in the area of automated model-checking algorithms. In turn, practical implementations of model-checking algorithms have enabled protocol developers to prove the correctness of such distributed protocols. However, model-checking techniques are only marginally useful during the actual development of such protocols; typically as a debugging aid once a reasonably complete version of the protocol has already been developed. The actual development process itself is often tedious and requires the designer to reason about complex interactions arising out of concurrency and asynchrony inherent to such protocols. In this dissertation we describe program synthesis techniques which can be applied as an enabling technology to ease the task of developing such protocols. Specifically, the programmer provides a natural, but incomplete description of the protocol in an intuitive representation — such as scenarios or an incomplete protocol. This description specifies the behavior of the protocol in the common cases. The programmer also specifies a set of high-level formal requirements that a correct protocol is expected to satisfy. These requirements can include safety requirements as well as liveness requirements in the
form of Linear Temporal Logic (LTL) formulas. We describe techniques to synthesize a correct protocol which is consistent with the common-case behavior specified by the programmer and also satisfies the high-level safety and liveness requirements set forth by the programmer. We also describe techniques for program synthesis in general, which serve to enable the solutions to distributed protocol synthesis that this dissertation explores
One-dimensional spin-orbit coupled Dirac system with extended -wave superconductivity: Majorana modes and Josephson effects
Motivated by the spin-momentum locking of electrons at the boundaries of
topological insulators, we study a one-dimensional system of spin-orbit coupled
massless Dirac electrons with -wave superconducting pairing. As a result of
the spin-orbit coupling, our model has only two kinds of linearly dispersing
modes, which we take to be right-moving spin-up and left-moving spin-down. Both
lattice and continuum models are studied. In the lattice model, we find that a
single Majorana zero energy mode appears at each end of a finite system
provided that the -wave pairing has an extended form, with the
nearest-neighbor pairing being larger than the on-site pairing. We confirm this
both numerically and analytically by calculating the winding number. Next we
study a lattice version of a model with both Schr\"odinger and Dirac-like terms
and find that the model hosts a topological transition between topologically
trivial and non-trivial phases depending on the relative strength of the
Schr\"odinger and Dirac terms. We then study a continuum system consisting of
two -wave superconductors with different phases of the pairing. Remarkably,
we find that the system has a {\it single} Andreev bound state which is
localized at the junction. When the pairing phase difference crosses a multiple
of , an Andreev bound state touches the top of the superconducting gap
and disappears, and a different state appears from the bottom of the gap. We
also study the AC Josephson effect in such a junction with a voltage bias that
has both a constant and a term which oscillates with a frequency
. We find that, in contrast to standard Josephson junctions, Shapiro
plateaus appear when the Josephson frequency is a
rational fraction of . We discuss experiments which can realize such
junctions.Comment: 16 pages, 9 figures; made some significant changes, added a figure
and several reference
Synthesizing Attack-Aware Control and Active Sensing Strategies under Reactive Sensor Attacks
We consider the probabilistic planning problem for a defender (P1) who can
jointly query the sensors and take control actions to reach a set of goal
states while being aware of possible sensor attacks by an adversary (P2) who
has perfect observations. To synthesize a provably correct, attack-aware
control and active sensing strategy for P1, we construct a stochastic game on
graph where the augmented state includes the actual game state (known by the
attacker), the belief of the defender about the game state (constructed by the
attacker given the attacker's information about the defender's information). We
presented an algorithm to solve a belief-based, randomized strategy for P1 to
ensure satisfying P1's reachability objective with probability one, under the
worst case sensor attacks carried out by an informed P2. The correctness of the
algorithm is proven and illustrated with an example.Comment: 6 pages, 1 figure, 1 table, 1 algorith
Syntax-guided synthesis
The classical formulation of the program-synthesis problem is to find a program that meets a correctness specification given as a logical formula. Recent work on program synthesis and program optimization illustrates many potential benefits of allowing the user to supplement the logical specification with a syntactic template that constrains the space of allowed implementations. Our goal is to identify the core computational problem common to these proposals in a logical framework. The input to the syntax-guided synthesis problem (SyGuS) consists of a background theory, a semantic correctness specification for the desired program given by a logical formula, and a syntactic set of candidate implementations given by a grammar. The computational problem then is to find an implementation from the set of candidate expressions so that it satisfies the specification in the given theory. We describe three different instantiations of the counter-example-guided-inductive-synthesis (CEGIS) strategy for solving the synthesis problem, report on prototype implementations, and present experimental results on an initial set of benchmarks.National Science Foundation (U.S.) (Expeditions in Computing Project ExCAPE Award CCF 1138996