Efficient Synthesis Algorithm Research Articles

Probabilistic Unitary Synthesis with Optimal Accuracy

The purpose of unitary synthesis is to find a gate sequence that optimally approximates a target unitary transformation. A new synthesis approach, called probabilistic synthesis, has been introduced, and its superiority has been demonstrated over traditional deterministic approaches with respect to approximation error and gate length. However, the optimality of current probabilistic synthesis algorithms is unknown. We obtain the tight lower bound on the approximation error obtained by the optimal probabilistic synthesis, which guarantees the sub-optimality of current algorithms. We also show its tight upper bound, which improves and unifies current upper bounds depending on the class of target unitaries. These two bounds reveal the fundamental relationship of approximation error between probabilistic approximation and deterministic approximation of unitary transformations. From a computational point of view, we show that the optimal probability distribution can be computed by the semidefinite program (SDP) we construct. We also construct an efficient probabilistic synthesis algorithm for single-qubit unitaries, rigorously estimate its time complexity, and show that it reduces the approximation error quadratically compared with deterministic algorithms.

Programming by Example Made Easy

Programming by example (PBE) is an emerging programming paradigm that automatically synthesizes programs specified by user-provided input-output examples. Despite the convenience for end-users, implementing PBE tools often requires strong expertise in programming language and synthesis algorithms. Such a level of knowledge is uncommon among software developers. It greatly limits the broad adoption of PBE by the industry. To facilitate the adoption of PBE techniques, we propose a PBE framework called Bee , which leverages an “entity-action” model based on relational tables to ease PBE development for a wide but restrained range of domains. Implementing PBE tools with Bee only requires adapting domain-specific data entities and user actions to tables, with no need to design a domain-specific language or an efficient synthesis algorithm. The synthesis algorithm of Bee exploits bidirectional searching and constraint-solving techniques to address the challenge of value computation nested in table transformation. We evaluated Bee ’s effectiveness on 64 PBE tasks from three different domains and usability with a human study of 12 participants. Evaluation results show that Bee is easier to learn and use than the state-of-the-art PBE framework, and the bidirectional algorithm achieves comparable performance to domain-specifically optimized synthesizers.

A normal form for single-qudit Clifford+T operators

Normal forms play a crucial role in the problem of gate synthesis. We propose a normal form for single-qudit gates composed of Clifford and T-gates for qudits of odd prime dimension $$p\ge 5$$ . We prove that any single-qudit Clifford+T operator can be re-expressed in this normal form in polynomial time. We obtained strong computational evidence that this normal form is unique. Assuming uniqueness, we are able to use this normal form to provide an efficient algorithm for exact synthesis of any single-qudit Clifford+T operator with minimal T-count.

Wide-viewing full-color depthmap computer-generated holograms.

An efficient synthesis algorithm for wide-viewing full-color depthmap computer-generated holograms is proposed. We develop a precise computational algorithm integrating wave-optic geometry-mapping, color-matching, and noise-filtering to multiplex multiview elementary computer-generated holograms (CGHs) into a single high-definition CGH without three-dimensional perspective distortion or color dispersion. Computational parallelism is exploited to achieve significant computational efficiency improvement in the production throughput of full-color wide-viewing angle CGHs. The proposed algorithm is verified through the full-color binary hologram reconstruction experiments utilizing an off-axis R·G·B simultaneous illumination method, which suggests the feasibility of the full-color sub-wavelength binary spatial light modulator technology.

Optimal two-qubit circuits for universal fault-tolerant quantum computation

We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS = diag(1, 1, 1, i). The Clifford+CS gate set is universal for quantum computation and its elements can be implemented fault-tolerantly in most error-correcting schemes through magic state distillation. Since non-Clifford gates are typically more expensive to perform in a fault-tolerant manner, it is often desirable to construct circuits that use few CS gates. In the present paper, we introduce an efficient and optimal synthesis algorithm for two-qubit Clifford+CS operators. Our algorithm inputs a Clifford+CS operator U and outputs a Clifford+CS circuit for U, which uses the least possible number of CS gates. Because the algorithm is deterministic, the circuit it associates to a Clifford+CS operator can be viewed as a normal form for that operator. We give an explicit description of these normal forms and use this description to derive a worst-case lower bound of 5{{rm{log}}}_{2}(frac{1}{epsilon })+O(1) on the number of CS gates required to ϵ-approximate elements of SU(4). Our work leverages a wide variety of mathematical tools that may find further applications in the study of fault-tolerant quantum circuits.

WebRelate: integrating web data with spreadsheets using examples

Data integration between web sources and relational data is a key challenge faced by data scientists and spreadsheet users. There are two main challenges in programmatically joining web data with relational data. First, most websites do not expose a direct interface to obtain tabular data, so the user needs to formulate a logic to get to different webpages for each input row in the relational table. Second, after reaching the desired webpage, the user needs to write complex scripts to extract the relevant data, which is often conditioned on the input data. Since many data scientists and end-users come from diverse backgrounds, writing such complex regular-expression based logical scripts to perform data integration tasks is unfortunately often beyond their programming expertise. We present WebRelate, a system that allows users to join semi-structured web data with relational data in spreadsheets using input-output examples. WebRelate decomposes the web data integration task into two sub-tasks of i) URL learning and ii) input-dependent web extraction. We introduce a novel synthesis paradigm called "Output-constrained Programming By Examples", which allows us to use the finite set of possible outputs for the new inputs to efficiently constrain the search in the synthesis algorithm. We instantiate this paradigm for the two sub-tasks in WebRelate. The first sub-task generates the URLs for the webpages containing the desired data for all rows in the relational table. WebRelate achieves this by learning a string transformation program using a few example URLs. The second sub-task uses examples of desired data to be extracted from the corresponding webpages and learns a program to extract the data for the other rows. We design expressive domain-specific languages for URL generation and web data extraction, and present efficient synthesis algorithms for learning programs in these DSLs from few input-output examples. We evaluate WebRelate on 88 real-world web data integration tasks taken from online help forums and Excel product team, and show that WebRelate can learn the desired programs within few seconds using only 1 example for the majority of the tasks.

FIDEX: filtering spreadsheet data using examples

Data filtering in spreadsheets is a common problem faced by millions of end-users. The task of data filtering requires a computational model that can separate intended positive and negative string instances. We present a system, FIDEX, that can efficiently learn desired data filtering expressions from a small set of positive and negative string examples. There are two key ideas of our approach. First, we design an expressive DSL to represent disjunctive filter expressions needed for several real-world data filtering tasks. Second, we develop an efficient synthesis algorithm for incrementally learning consistent filter expressions in the DSL from very few positive and negative examples. A DAG-based data structure is used to succinctly represent a large number of filter expressions, and two corresponding operators are defined for algorithmically handling positive and negative examples, namely, the intersection and subtraction operators. FIDEX is able to learn data filters for 452 out of 460 real-world data filtering tasks in real time (0.22s), using only 2.2 positive string instances and 2.7 negative string instances on average.

Symbolic On-the-Fly Synthesis in Supervisory Control Theory

This paper presents an efficient synthesis algorithm and its proof of correctness for computing the controllable, nonblocking, and minimally restrictive supervisor in the supervisory control theory. Conventional synthesis algorithms are based on backward reachability computations, where blocking and uncontrollable states are iteratively found by searching the entire state space several times until a fixed point is reached. Many unnecessary states may be visited in this kind of searching. In this paper, we present an alternative synthesis algorithm based on forward reachability, where a number of synthesis steps are performed during the reachability computations. This approach is inspired from the search techniques in Artificial Intelligence (AI) planning. To handle large-scale problems, the algorithm performs the computations symbolically based on binary decision diagrams . The algorithm has been developed, implemented, and applied to several large-scale benchmarks. It is shown that, on average, the on-the-fly algorithm is more efficient than the conventional synthesis algorithms, in particular for problems with many uncontrollable states.

Dynamic Controllability of Disjunctive Temporal Networks: Validation and Synthesis of Executable Strategies

The Temporal Network with Uncertainty (TNU) modeling framework is used to represent temporal knowledge in presence of qualitative temporal uncertainty. Dynamic Controllability (DC) is the problem of deciding the existence of a strategy for scheduling the controllable time points of the network observing past happenings only. In this paper, we address the DC problem for a very general class of TNU, namely Disjunctive Temporal Network with Uncertainty. We make the following contributions. First, we define strategies in the form of an executable language; second, we propose the first decision procedure to check whether a given strategy is a solution for the DC problem; third we present an efficient algorithm for strategy synthesis based on techniques derived from Timed Games and Satisfiability Modulo Theory. The experimental evaluation shows that the approach is superior to the state-of-the-art.

A multi-paradigm language for reactive synthesis

This paper proposes a language for describing reactive synthesis problems that integrates imperative and declarative elements. The semantics is defined in terms of two-player turn-based infinite games with full information. Currently, synthesis tools accept linear temporal logic (LTL) as input, but this description is less structured and does not facilitate the expression of sequential constraints. This motivates the use of a structured programming language to specify synthesis problems. Transition systems and guarded commands serve as imperative constructs, expressed in a syntax based on that of the modeling language Promela. The syntax allows defining which player controls data and control flow, and separating a program into assumptions and guarantees. These notions are necessary for input to game solvers. The integration of imperative and declarative paradigms allows using the paradigm that is most appropriate for expressing each requirement. The declarative part is expressed in the LTL fragment of generalized reactivity(1), which admits efficient synthesis algorithms, extended with past LTL. The implementation translates Promela to input for the Slugs synthesizer and is written in Python. The AMBA AHB bus case study is revisited and synthesized efficiently, identifying the need to reorder binary decision diagrams during strategy construction, in order to prevent the exponential blowup observed in previous work.

Design and analysis of efficient synthesis algorithms for EDAC functions in FPGAs

Error detection and correction (EDAC) functions have been widely used for protecting memories from single event upsets (SEU), which occur in environments with high levels of radiation or in deep submicron manufacturing technologies. This paper presents three novel synthesis algorithms that obtain area-efficient implementations for a given EDAC function, with the ultimate aim of reducing the number of sensitive configuration bits in SRAM-based field-programmable gate arrays (FPGAs). Having less sensitive bits results in a lower chance of suffering an SEU in the EDAC circuitry, thus improving the overall reliability of the whole system. Besides minimizing area, the proposed algorithms also focus on improving other figures of merit like circuit speed and power consumption. The executed benchmarks show that, when compared with other modern synthesis tools, the proposed algorithms can reduce the number of utilized look-up tables (LUTs) up to a 34.48%. Such large reductions in area usage ultimately result in reliability improvements over 10% for the implemented EDAC cores, measured as MTBF (mean time between failures). On the other hand, maximum path delays and power consumptions can be reduced up to a 17.72% and 34.37%, respectively, on the placed and routed designs.

Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets

We generalize an efficient exact synthesis algorithm for single-qubit unitaries over the Clifford+T gate set which was presented by Kliuchnikov, Maslov, and Mosca [Quantum Inf. Comput. 13(7,8), 607–630 (2013)]. Their algorithm takes as input an exactly synthesizable single-qubit unitary—one which can be expressed without error as a product of Clifford and T gates—and outputs a sequence of gates which implements it. The algorithm is optimal in the sense that the length of the sequence, measured by the number of T gates, is smallest possible. In this paper, for each positive even integer n, we consider the “Clifford-cyclotomic” gate set consisting of the Clifford group plus a z-rotation by πn. We present an efficient exact synthesis algorithm which outputs a decomposition using the minimum number of πn z-rotations. For the Clifford+T case n = 4, the group of exactly synthesizable unitaries was shown to be equal to the group of unitaries with entries over the ring Z[eiπn,1/2]. We prove that this characterization holds for a handful of other small values of n but the fraction of positive even integers for which it fails to hold is 100%.

Gradient-Domain Bidirectional Path Tracing

Gradient-domain path tracing has recently been introduced as an efficient realistic image synthesis algorithm. This paper introduces a bidirectional gradient-domain sampler that outperforms traditional bidirectional path tracing often by a factor of two to five in terms of squared error at equal render time. It also improves over unidirectional gradient-domain path tracing in challenging visibility conditions, similarly as conventional bidirectional path tracing improves over its unidirectional counterpart. Our algorithm leverages a novel multiple importance sampling technique and an efficient implementation of a high-quality shift mapping suitable for bidirectional path tracing. We demonstrate the versatility of our approach in several challenging light transport scenarios.

Efficient Active Learning of Halfspaces via Query Synthesis

Active learning is a subfield of machine learning that has been successfully used in many applications including text classification and bioinformatics. One of the fundamental branches of active learning is query synthesis, where the learning agent constructs artificial queries from scratch in order to reveal sensitive information about the true decision boundary. Nevertheless, the existing literature on membership query synthesis has focused on finite concept classes with a limited extension to real-world applications. In this paper, we present an efficient spectral algorithm for membership query synthesis for halfspaces, whose sample complexity is experimentally shown to be near-optimal. At each iteration, the algorithm consists of two steps. First, a convex optimization problem is solved that provides an approximate characterization of the version space. Second, a principal component is extracted, which yields a synthetic query that shrinks the version space exponentially fast. Unlike traditional methods in active learning, the proposed method can be readily extended into the batch setting by solving for the top k eigenvectors in the second step. Experimentally, it exhibits a significant improvement over traditional approaches such as uncertainty sampling and representative sampling. For example, to learn a halfspace in the Euclidean plane with 25 dimensions and an estimation error of 1E-4, the proposed algorithm uses less than 3% of the number of queries required by uncertainty sampling.

Qinghai-Tibet Plateau crustal thickness derived from EGM2008 and CRSUT2.0

Abstract: Qinghai-Tibet Plateau is the most complex region for crustal thickness inversion, while high-resolution earth gravity model (EGM) makes it possible to obtain high precision gravity anomaly, which is a key parameter to depict the Earth’s inner structure in geodesy domain. On the basis of this principle, we calculated the Bouguer gravity anomalies in Qinghai-Tibet Plateau with EGM2008 and SRTM6. 0 by efficient high-degree spherical harmonic synthesis algorithm. In order to obtain the gravity anomaly caused by Moho density mutant, the noises caused by the topography was removed by wavelet details. Then, the crustal thickness was corrected on the basis of CRUST 2. 0 with the deep-large-scale single density interface formula. The inversion result indicates that the crustal thickness in Qinghai-Tibet Plateau is between 50 km and 75 km, which is in correspondence with the recent science research result. Compared with the 2 degree CRUST 2. 0 model, the spatial resolution of crustal thickness in our research can reach 40 arc minutes. In addition, there is a positive relationship between the inversed crustal thickness and topography, which can prove the effectiveness of Airy-Heiskanen isostatic model in gravity reduction.

Realization of a new permutative gate library using controlled-kth-root-of-NOT quantum gates for exact minimization of quantum circuits

Since non-permutative quantum gates have more complex rules than permutative quantum gates, it is very hard to synthesize quantum logic circuits using non-permutative quantum gates, such as controlled-square-root-of-NOT gates (CV∕CV+ gates). In the efficient synthesis algorithm, direct use of quantum non-permutative gates should be avoided. Rather, the key method is to use quantum gates to create new permutative quantum gates that then replace non-permutative quantum gates. This method assumes the library of quantum gate primitives are constructed so as to have the lowest possible quantum cost. In this paper, we first propose some new CV∕CV+-like gates, i.e. controlled-kth-root-of-NOT gates where k = 2,4,8,…, and give all corresponding matrixes. Further, we also present a novel generic method to quickly and directly construct this new optimal quantum logic gate library using CNOT and these non-permutative quantum gates. Our method introduces new means to find permutative quantum gates with lower quantum cost.

Efficient synthesis of feature models

ContextVariability modeling, and in particular feature modeling, is a central element of model-driven software product line architectures. Such architectures often emerge from legacy code, but, creating feature models from large, legacy systems is a long and arduous task. We describe three synthesis scenarios that can benefit from the algorithms in this paper. ObjectiveThis paper addresses the problem of automatic synthesis of feature models from propositional constraints. We show that the decision version of the problem is NP-hard. We designed two efficient algorithms for synthesis of feature models from CNF and DNF formulas respectively. MethodWe performed an experimental evaluation of the algorithms against a binary decision diagram (BDD)-based approach and a formal concept analysis (FCA)-based approach using models derived from realistic models. ResultsOur evaluation shows a 10 to 1,000-fold performance improvement for our algorithms over the BDD-based approach. The performance of the DNF-based algorithm was similar to the FCA-based approach, with advantages for both techniques. We identified input properties that affect the runtimes of the CNF- and DNF-based algorithms. ConclusionsOur algorithms are the first known techniques that are efficient enough to be used on dependencies extracted from real systems, opening new possibilities of creating reverse engineering and model management tools for variability models.

Efficient controller synthesis for a fragment of $$\hbox {MTL}_{0, \infty }$$ MTL 0 , ∞

In this paper we offer an efficient controller synthesis algorithm for assume-guarantee specifications of the form $$\varphi _1 \wedge \varphi _2 \wedge \cdots \wedge \varphi _n \rightarrow \psi _1 \wedge \psi _2 \wedge \cdots \wedge \psi _m$$ . Here, $$\{\varphi _i,\psi _j\}$$ are all safety-MTL $$_{0, \infty }$$ properties, where the sub-formulas $$\{\varphi _i\}$$ are supposed to specify assumptions of the environment and the sub-formulas $$\{\psi _j\}$$ are specifying requirements to be guaranteed by the controller. Our synthesis method exploits the engine of Uppaal-Tiga and the novel translation of safety- and co-safety-MTL $$_{0, \infty }$$ properties into under-approximating, deterministic timed automata. Our approach avoids determinization of Buchi automata, which is the main obstacle for the practical applicability of controller synthesis for linear-time specifications. The experiments demonstrate that the chosen specification formalism is expressive enough to specify complex behaviors. The proposed approach is sound but not complete. However, it successfully produced solutions for all the experiments. Additionally we compared our tool with Acacia+ and Unbeast, state-of-the-art LTL synthesis tools; and our tool demonstrated better timing results, when we applied both tools to the analogous specifications.

Efficient algorithm for simultaneous synthesis of heat exchanger networks

The mathematical programming based simultaneous approaches for heat exchanger network synthesis (HENS) result in large, complex, non-convex mixed-integer nonlinear programming (MINLP) models, for which finding even a feasible solution is a challenge. We propose a tailor-made search strategy that repeatedly revives the outer approximation (OA) algorithm of Viswanathan and Grossmann (1990), which in its original form is mostly ineffective for solving large HENS problems. We propose three smaller and simpler perturbations of the master problem in the OA algorithm by prioritizing, fixing, eliminating, or limiting exchangers in various ways to avoid premature termination. Our approach needs no feasible starting point, and solves much faster and better than some commercial MINLP solvers. We illustrate the application of our strategy with two recent HENS models on seven literature examples with up to 39 process streams. The algorithm solves them very efficiently and obtains solutions as good or better than those reported in the literature. Its robustness and effectiveness are exemplified by a large literature problem involving 39 process streams, where it obtains a 0.32% better solution than the best reported in the literature via a genetic algorithm.

Synthesis of antenna arrays with an efficient multiobjective differential evolution algorithm

An efficient multiobjective differential evolution algorithm for array synthesis is proposed in this article. By introducing novel strategies in the generalized differential evolution GDE3, the proposed algorithm can generate a better converged and distributed Pareto front than the standard GDE3. Five typical benchmark functions are optimized by the proposed improved GDE3 IGDE to verify its effectiveness. Furthermore, the proposed algorithm is applied in two-pattern synthesis problems, including an unequal spaced linear array and a conformal array. The superior performance of the proposed IGDE demonstrates that it is an efficient and competitive algorithm in the function optimization, pattern synthesis, and other electromagnetic problems. © 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE 24:161-169, 2014.