# Sicun Gao's research while affiliated with University of California, San Diego and other places

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## Publications (56)

Path-tracking control of self-driving vehicles can benefit from deep learning for tackling longstanding challenges such as nonlinearity and uncertainty. However, deep neural controllers lack safety guarantees, restricting their practical use. We propose a new approach of learning almost-barrier functions, which approximately characterizes the forwa...

User embeddings (vectorized representations of a user) are essential in recommendation systems. Numerous approaches have been proposed to construct a representation for the user in order to find similar items for retrieval tasks, and they have been proven effective in industrial recommendation systems as well. Recently people have discovered the po...

Long Short-Term Memory (LSTM) and Transformers are two popular neural architectures used for natural language processing tasks. Theoretical results show that both are Turing-complete and can represent any context-free language (CFL).In practice, it is often observed that Transformer models have better representation power than LSTM. But the reason...

Learning-enabled control systems have demonstrated impressive empirical performance on challenging control problems in robotics, but this performance comes at the cost of reduced transparency and lack of guarantees on the safety or stability of the learned controllers. In recent years, new techniques have emerged to provide these guarantees by lear...

Long Short-Term Memory (LSTM) and Transformers are two popular neural architectures used for natural language processing tasks. Theoretical results show that both are Turing-complete and can represent any context-free language (CFL).In practice, it is often observed that Transformer models have better representation power than LSTM. But the reason...

Safety and stability are common requirements for robotic control systems; however, designing safe, stable controllers remains difficult for nonlinear and uncertain models. We develop a model-based learning approach to synthesize robust feedback controllers with safety and stability guarantees. We take inspiration from robust convex optimization and...

The lack of stability guarantee restricts the practical use of learning-based methods in core control problems in robotics. We develop new methods for learning neural control policies and neural Lyapunov critic functions in the model-free reinforcement learning (RL) setting. We use sample-based approaches and the Almost Lyapunov function conditions...

Many-tier vertical gate-all-around nanowire FET (VFET) synthesis strongly demands a holistic approach of modeling/formulating/optimizing transistor placement and in-cell routing to obtain the maximum-achievable PPAC (power, performance, area, and cost) benefits. In this paper, we propose a novel SMT (Satisfiability Modulo Theories)-based many-tier...

With relentless scaling of technology nodes, the design technology co-optimization (DTCO) requires prompt development of standard cell libraries to explore the scaling effects of various cell architectures. However, standard cell synthesis demands holistic considerations for transistor placement, in-cell routing, and pin-accessibility due to the li...

We propose new methods for learning control policies and neural network Lyapunov functions for nonlinear control problems, with provable guarantee of stability. The framework consists of a learner that attempts to find the control and Lyapunov functions, and a falsifier that finds counterexamples to quickly guide the learner towards solutions. The...

Pin accessibility encounters non-trivial challenges due to the smaller number of routing tracks, higher pin density, and more complex design rules. Consequently, securing design rule-correct routability has become a critical bottleneck for sub-10nm IC designs (particularly in the detailed routing stage) costing days of runtime. To reduce turnaround...

We present VeriSketch, a security-oriented program synthesis framework for developing hardware designs with formal guarantee of functional and security specifications. VeriSketch defines a synthesis language, a code instrumentation framework for specifying and inferring timing-sensitive information flow properties, and uses specialized constraint-b...

Interval Constraint Propagation (ICP) is a powerful method for solving general nonlinear constraints over real numbers. ICP uses interval arithmetic to prune the space of potential solutions and, when the constraint propagation fails, divides the space into smaller regions and continues recursively. The original goal is to find paving boxes of all...

Neural networks in real-world applications have to satisfy critical properties such as safety and reliability. The analysis of such properties typically requires extracting information through computing pre-images of the network transformations, but it is well-known that explicit computation of pre-images is intractable. We introduce new methods fo...

We formulate numerically-robust inductive proof rules for unbounded stability and safety properties of continuous dynamical systems. These induction rules robustify standard notions of Lyapunov functions and barrier certificates so that they can tolerate small numerical errors. In this way, numerically-driven decision procedures can establish a sou...

Routability diagnosis has increasingly become the bottleneck in detailed routing for sub-10nm technology due to the limited tracks, high density, and complex design rules. The conventional ways to examine the routability of detailed routing are ILP- and SAT-based techniques. However, once we identify the routability, the diagnosis remains an open p...

Neural networks in real-world applications have to satisfy critical properties such as safety and reliability. The analysis of such properties typically requires extracting information through computing pre-images of the network transformations, but it is well-known that explicit computation of pre-images is intractable. We introduce new methods fo...

We propose new methods for learning control policies and neural network Lyapunov functions for nonlinear control problems, with provable guarantee of stability. The framework consists of a learner that attempts to find the control and Lyapunov functions, and a falsifier that finds counterexamples to quickly guide the learner towards solutions. The...

We introduce continuous Lagrangian reachability (CLRT), a new algorithm for the computation of a tight and continuous-time reachtube for the solution flows of a nonlinear, time-variant dynamical system. CLRT employs finite strain theory to determine the deformation of the solution set from time $t_i$ to time $t_{i+1}$. We have developed simple expl...

Solving nonlinear SMT problems over real numbers has wide applications in robotics and AI. While significant progress is made in solving quantifier-free SMT formulas in the domain, quantified formulas have been much less investigated. We propose the first delta-complete algorithm for solving satisfiability of nonlinear SMT over real numbers with un...

We propose \(\delta \)-complete decision procedures for solving satisfiability of nonlinear SMT problems over real numbers that contain universal quantification and a wide range of nonlinear functions. The methods combine interval constraint propagation, counterexample-guided synthesis, and numerical optimization. In particular, we show how to hand...

In this paper, we present ReaS, a technique that combines numerical optimization with SAT solving to synthesize unknowns in a program that involves discrete and floating point computation. ReaS makes the program end-to-end differentiable by smoothing any Boolean expression that introduces discontinuity such as conditionals and relaxing the Boolean...

The Author(s) 2018. We propose δ -complete decision procedures for solving satisfiability of nonlinear SMT problems over real numbers that contain universal quantification and a wide range of nonlinear functions. The methods combine interval constraint propagation, counterexample-guided synthesis, and numerical optimization. In particular, we show...

Neural networks are highly sensitive to adversarial examples, which cause large output deviations with only small input perturbations. However, little is known quantitatively about the distribution and prevalence of such adversarial examples. To address this issue, we propose a rigorous search method that provably finds the smallest possible advers...

We propose a new abstraction refinement procedure based on machine learning to improve the performance of nonlinear constraint solving algorithms on large-scale problems. The proposed approach decomposes the original set of constraints into smaller subsets, and uses learning algorithms to propose sequences of abstractions that take the form of conj...

Some industrial systems are difficult to formally verify due to their large scale. In particular, the widespread use of lookup tables in embedded systems across diverse industries, such as aeronautics and automotive systems, create a critical obstacle to the scalability of formal verification. This paper presents Osiris, a tool that automatically c...

Modern safety-critical systems are difficult to formally verify, largely due to their large scale. In particular, the widespread use of lookup tables in embedded systems across diverse industries, such as aeronautics and automotive systems, create a critical obstacle to the scalability of formal verification. This paper presents a novel approach fo...

This work addresses the problem of scalable constraint solving. Our technique combines traditional constraint-solving approaches with machine learning techniques to propose abstractions that simplify the problem. First, we use a collection of heuristics to learn sets of constraints that may be well abstracted as a single, simpler constraint. Next,...

This paper presents general techniques for verifying virtually synchronous distributed control systems with interconnected physical environments. Such cyber-physical systems (CPSs) are notoriously hard to verify, due to their combination of nontrivial continuous dynamics, network delays, imprecise local clocks, asynchronous communication, etc. To s...

Autonomous vehicles (AVs) have already driven millions of miles on public roads, but even the simplest scenarios have not been certified for safety. Current methodologies for the verification of AV's decision and control systems attempt to divorce the lower level, short-term trajectory planning and trajectory tracking functions from the behavioral...

In this paper, we present a new tool SReach, which solves probabilistic bounded reachability problems for two classes of models of stochastic hybrid systems. The first one is (nonlinear) hybrid automata with parametric uncertainty. The second one is probabilistic hybrid automata with additional randomness for both transition probabilities and varia...

dReach is a bounded reachability analysis tool for nonlinear hybrid systems. It encodes reachability problems of hybrid systems to first-order formulas over real numbers, which are solved by delta-decision procedures in the SMT solver dReach. In this way, dReach is able to handle a wide range of highly nonlinear hybrid systems. It has scaled well o...

Recent clinical studies suggest that the efficacy of hormone therapy for
prostate cancer depends on the characteristics of individual patients. In this
paper, we develop a computational framework for identifying patient-specific
androgen ablation therapy schedules for postponing the potential cancer
relapse. We model the population dynamics of hete...

The design of bug-free and safe medical device software is challenging, especially in complex implantable devices that control and actuate organs who’s response is not fully understood. Safety recalls of pacemakers and implantable cardioverter defibrillators between 1990 and 2000 affected over 600,000 devices. Of these, 200,000 or 41%, were due to...

Rapid progress in modern medical technologies has led to a new generation of healthcare devices and treatment strategies. Examples include electro-anatomical mapping and intervention, bio-compatible and implantable devices, minimally invasive embedded devices, and robotic prosthetics.

We present the framework of delta-complete analysis for bounded reachability problems of hybrid systems. We perform bounded reachability checking through solving delta-decision problems over the reals. The techniques take into account of robustness properties of the systems under numerical perturbations. Our implementation of the techniques scales...

We show how to generate and validate logical proofs of unsatisfiability from
delta-complete decision procedures that rely on error-prone numerical
algorithms. Solving this problem is important for ensuring correctness of the
decision procedures. At the same time, it is a new approach for automated
theorem proving over real numbers. We design a firs...

A central problem in systems biology is to identify parameter values such
that a biological model satisfies some behavioral constraints (\eg, time
series). In this paper we focus on parameter synthesis for hybrid
(continuous/discrete) models, as many biological systems can possess multiple
operational modes with specific continuous dynamics in each...

We develop a framework to give upper bounds on the "practical" computational
complexity of stability problems for a wide range of nonlinear continuous and
hybrid systems. To do so, we describe stability properties of dynamical systems
using first-order formulas over the real numbers, and reduce stability problems
to the delta-decision problems of t...

We present a novel approach for solving the probabilistic bounded
reachability problem of hybrid systems with parameter uncertainty. Standard
approaches to this problem require numerical solutions for large optimization
problems, and become unfeasible for systems involving nonlinear dynamics over
the reals. Our approach combines randomized sampling...

We present the framework of delta-complete analysis for bounded reachability
problems of general hybrid systems. We perform bounded reachability checking
through solving delta-decision problems over the reals. The techniques take
into account of robustness properties of the systems under numerical
perturbations. We prove that the verification probl...

We study SMT problems over the reals containing ordinary differential
equations. They are important for formal verification of realistic hybrid
systems and embedded software. We develop delta-complete algorithms for SMT
formulas that are purely existentially quantified, as well as exists-forall
formulas whose universal quantification is restricted...

A system and method for deciding the satisfiability of a non-linear real decision problem is disclosed. Linear and non-linear constraints associated with the problem are separated. The feasibility of the linear constraints is determined using a linear solver. The feasibility of the non-linear constraints is determined using a non-linear solver whic...

We describe the open-source tool dReal, an SMT solver for nonlinear formulas over the reals. The tool can handle various nonlinear real functions such as polynomials, trigonometric functions, exponential functions, etc. dReal implements the framework of δ-complete decision procedures: It returns either unsat or δ
-sat on input formulas, where δ is...

Given any collection F of computable functions over the reals, we show that
there exists an algorithm that, given any L_F-sentence \varphi containing only
bounded quantifiers, and any positive rational number \delta, decides either
"\varphi is true", or "a \delta-strengthening of \varphi is false". Under mild
assumptions, for a C-computable signatu...

We introduce the notion of "\delta-complete decision procedures" for solving
SMT problems over the real numbers, with the aim of handling a wide range of
nonlinear functions including transcendental functions and solutions of
Lipschitz-continuous ODEs. Given an SMT problem \varphi and a positive rational
number \delta, a \delta-complete decision pr...

We give an algebraic quantifier elimination algorithm for the first-order
theory over any given finite field using Gr\"obner basis methods. The algorithm
relies on the strong Nullstellensatz and properties of elimination ideals over
finite fields. We analyze the theoretical complexity of the algorithm and show
its application in the formal analysis...

We describe a DPLL-based solver for the problem of quantified boolean formulas (QBF) in non-prenex, non-CNF form. We make
two contributions. First, we reformulate clause/cube learning, extending it to non-prenex instances. We call the resulting
technique game-state learning. Second, we introduce a propagation technique using ghost literals that exp...

We propose a novel integration of interval constraint propagation (ICP) with SMT solvers for linear real arithmetic (LRA) to decide nonlinear real arithmetic problems. We use ICP to search for interval solutions of the nonlinear constraints, and use the LRA solver to either validate the solutions or provide constraints to incrementally refine the s...

## Citations

... It could be said that alike LSTM and Transformer networks visualise context-free languages with constrained iteration and similar representation power. However, the disadvantage of the LSTM model is that it fails to factorise its innate area to encrypt the state and numerous aspects of the stack without clear and specific guidance, which is the main pillar to its vulnerable results in real-time projects and practice [12]. However, the lack of explicit breakdown normalisation has a slight effect on the Transformer [12]. ...

... Formal methods have been used to solve bounding problems [RS07,GAC12], constraint satisfaction problems [FHT + 07], and optimization problems [KSG18]. The literature is too large to cover here; [DS19] surveys some of the methods that are used in connection with the verification of cyber-physical systems. ...

Reference: Verified Optimization

... Then [22,23] propose a contraction-metric-based control framework, which extends neural networks to certificate learning for contraction metrics. Moreover, based on the framework proposed by Tsukamoto et al., [24,25,26,8] are used to address higher dimensional control problems. ...

... Additionally, increasingly the human-computer interaction (HCI) community has been pursuing centering worker well-being and needs within algorithmic management platforms or intervention designs [18,57,70]. Recently, there have been calls specifcally for expanding designs of technological systems by collaborating with and centering the ideas of low-powered workers who are mediated or managed by algorithmic systems [16,34]. ...

... Recently, Lee et al. [20] have proposed a Satisfiability Modulo Theories (SMT)-based SDC synthesis automation framework that simultaneously solves the place-and-route (P&R) problem without deploying any sequential procedures by using a novel dynamic pin allocation (DPA) approach, resulting in the generation of SDCs with optimal cell areas. However, this work is unsuitable for the VFET SDC generation due to the distinctive spatial cell structure. ...

... Since commonly-used standard cell libraries cannot meet all the requirements in some special scenarios [2][3][4][5], as an alternative solution, academia [6][7][8][9][10][11][12][13][14][15][16][17][18][19] and industry [5,[20][21][22][23] take continuous efforts to extend standard cell libraries with custom standard cells for their technology nodes and domain-specific designs. One of the potential sources of these custom standard cells is standard cell merging, which merges several existing standard cells into a new one with an optimized layout, as a simplified example shown in Fig. 1. ...

... Our framework performs routability-driven lexicographic multiple-objective optimization by implementing (i) Multi-Row Cell Area Minimization, (ii) Edge-Based Pin Separation and (iii) M2 Track use objectives, and (iv) Metal Length. We utilize five representative conditional design rules of [18], [19], which are minimum area rule (MAR), end-of-line (EOL), via rule (VR), and multi-pattern-aware design rules (i.e., parallel run-length (PRL)/step height rule (SHR)). The notations are shown in Table I. ...

... Authors in [39] use low-rank features of the high-dimensional system to train a recurrent neural network (RNN) to predict the control relevant quantities for MPC. Other authors have used structured neural network models inspired by classical linear time-varying state-space models [40], whereas some have proposed using convex neural architectures [41], graph neural networks [42], or stable neural networks based on Lyapunov functions [43]. In this work, we build on these trends and employ neural state space models as generic abstractions for learning nonlinear dynamics models of the controlled system. ...

... There has also been an interest in using program synthesis in hardware designs [17]. VeriSketch [5] exploits the power of program synthesis in hardware design. Our work is orthogonal to the objectives and techniques of VeriSketch: while VeriSketch secures hardware against timing attacks, we propose a hardware locking mechanism. ...

... Based on our results for both MNIST and CIFAR10 networks, we conclude that our obtained regions are robust and can capture adversarial examples generated by variations caused when transferring a synthesized adversarial example in real-world conditions. 9 RELATED WORK e work of Dathathri et al. (2019) uses symbolic interpolation to compute both an under-and an overapproximation of the set of inputs for which a given output property holds. e work of explores linear regions speci ed by the activation pa erns of neurons in the network. ...