Generating Datasets for Real-Time Scheduling on 5G New Radio.

A 5G system is an advanced solution for industrial wireless motion control. However, because the scheduling model of 5G new radio (NR) is more complicated than those of other wireless networks, existing real-time scheduling algorithms cannot be used to improve the 5G performance. This results in NR resources not being fully available for industrial systems. Supervised learning has been widely used to solve complicated problems, and its advantages have been demonstrated in multiprocessor scheduling. One of the main reasons why supervised learning has not been used for 5G NR scheduling is the lack of training datasets. Therefore, in this paper, we propose two methods based on optimization modulo theories (OMT) and satisfiability modulo theories (SMT) to generate training datasets for 5G NR scheduling. Our OMT-based method contains fewer variables than existing work so that the Z3 solver can find optimal solutions quickly. To further reduce the solution time, we transform the OMT-based method into an SMT-based method and tighten the search space of SMT based on three theorems and an algorithm. Finally, we evaluate the solution time of our proposed methods and use the generated dataset to train a supervised learning model to solve the 5G NR scheduling problem. The evaluation results indicate that our SMT-based method reduces the solution time by 74.7% compared to existing ones, and the supervised learning algorithm achieves better scheduling performance than other polynomial-time algorithms.

Synthesising Programs with Non-trivial Constants.

Program synthesis is the mechanised construction of software. One of the main difficulties is the efficient exploration of the very large solution space, and tools often require a user-provided syntactic restriction of the search space. While useful in general, such syntactic restrictions provide little help for the generation of programs that contain non-trivial constants, unless the user is able to provide the constants in advance. This is a fundamentally difficult task for state-of-the-art synthesisers. We propose a new approach to the synthesis of programs with non-trivial constants that combines the strengths of a counterexample-guided inductive synthesiser with those of a theory solver, exploring the solution space more efficiently without relying on user guidance. We call this approach CEGIS(T), where T is a first-order theory. We present two exemplars, one based on Fourier-Motzkin (FM) variable elimination and one based on first-order satisfiability. We demonstrate the practical value of CEGIS(T) by automatically synthesising programs for a set of intricate benchmarks. Additionally, we present a case study where we integrate CEGIS(T) within the mature synthesiser CVC4 and show that CEGIS(T) improves CVC4's results.

Bounded Model Checking for Metric Temporal Logic Properties of Timed Automata with Digital Clocks.

Metric temporal logic (MTL) is a popular real-time extension of linear temporal logic (LTL). This paper presents a new simple SAT-based bounded model-checking (SAT-BMC) method for MTL interpreted over discrete infinite timed models generated by discrete timed automata with digital clocks. We show a new translation of the existential part of MTL to the existential part of linear temporal logic with a new set of atomic propositions and present the details of the new translation. We compare the new method's advantages to the old method based on a translation of the hard reset LTL (HLTL). Our method does not need new clocks or new transitions. It uses only one path and requires a smaller number of propositional variables and clauses than the HLTL-based method. We also implemented the new method, and as a case study, we applied the technique to analyze several systems. We support the theoretical description with the experimental results demonstrating the method's efficiency.

Quantum Algorithm for Variant Maximum Satisfiability.

In this paper, we proposed a novel quantum algorithm for the maximum satisfiability problem. Satisfiability (SAT) is to find the set of assignment values of input variables for the given Boolean function that evaluates this function as TRUE or prove that such satisfying values do not exist. For a POS SAT problem, we proposed a novel quantum algorithm for the maximum satisfiability (MAX-SAT), which returns the maximum number of OR terms that are satisfied for the SAT-unsatisfiable function, providing us with information on how far the given Boolean function is from the SAT satisfaction. We used Grover's algorithm with a new block called quantum counter in the oracle circuit. The proposed circuit can be adapted for various forms of satisfiability expressions and several satisfiability-like problems. Using the quantum counter and mirrors for SAT terms reduces the need for ancilla qubits and realizes a large Toffoli gate that is then not needed. Our circuit reduces the number of ancilla qubits for the terms T of the Boolean function from T of ancilla qubits to ≈⌈log2⁡T⌉+1. We analyzed and compared the quantum cost of the traditional oracle design with our design which gives a low quantum cost.

Initial Solution Generation and Diversified Variable Picking in Local Search for (Weighted) Partial MaxSAT.

The (weighted) partial maximum satisfiability ((W)PMS) problem is an important generalization of the classic problem of propositional (Boolean) satisfiability with a wide range of real-world applications. In this paper, we propose an initialization and a diversification strategy to improve local search for the (W)PMS problem. Our initialization strategy is based on a novel definition of variables' structural entropy, and it aims to generate a solution that is close to a high-quality feasible one. Then, our diversification strategy picks a variable in two possible ways, depending on a parameter: continuing to pick variables with the best benefits or focusing on a clause with the greatest penalty and then selecting variables probabilistically. Based on these strategies, we developed a local search solver dubbed ImSATLike, as well as a hybrid solver ImSATLike-TT, and experimental results on (weighted) partial MaxSAT instances in recent MaxSAT Evaluations show that they outperform or have nearly the same performances as state-of-the-art local search and hybrid competitors, respectively, in general. Furthermore, we carried out experiments to confirm the individual impacts of each proposed strategy.

Boolean satisfiability in quantum compilation.

Quantum compilation is the task of translating a quantum algorithm implemented in a high-level quantum programming language into a technology-dependent instructions flow for a physical quantum computer. To tackle the large gap between the quantum program and the low-level instructions, quantum compilation is split into a multi-stage flow consisting of several layers of abstraction. Several different individual tasks have been proposed for the layers in the flow, many of them are NP-hard. In this article, we will describe the flow and we will propose algorithms based on Boolean satisfiability, which is a good match to tackle such computationally complex problems. This article is part of the theme issue 'Harmonizing energy-autonomous computing and intelligence'.

Energy Based Logic Mining Analysis with Hopfield Neural Network for Recruitment Evaluation.

An effective recruitment evaluation plays an important role in the success of companies, industries and institutions. In order to obtain insight on the relationship between factors contributing to systematic recruitment, the artificial neural network and logic mining approach can be adopted as a data extraction model. In this work, an energy based k satisfiability reverse analysis incorporating a Hopfield neural network is proposed to extract the relationship between the factors in an electronic (E) recruitment data set. The attributes of E recruitment data set are represented in the form of k satisfiability logical representation. We proposed the logical representation to 2-satisfiability and 3-satisfiability representation, which are regarded as a systematic logical representation. The E recruitment data set is obtained from an insurance agency in Malaysia, with the aim of extracting the relationship of dominant attributes that contribute to positive recruitment among the potential candidates. Thus, our approach is evaluated according to correctness, robustness and accuracy of the induced logic obtained, corresponding to the E recruitment data. According to the experimental simulations with different number of neurons, the findings indicated the effectiveness and robustness of energy based k satisfiability reverse analysis with Hopfield neural network in extracting the dominant attributes toward positive recruitment in the insurance agency in Malaysia.

Amazon Employees Resources Access Data Extraction via Clonal Selection Algorithm and Logic Mining Approach.

Amazon.com Inc. seeks alternative ways to improve manual transactions system of granting employees resources access in the field of data science. The work constructs a modified Artificial Neural Network (ANN) by incorporating a Discrete Hopfield Neural Network (DHNN) and Clonal Selection Algorithm (CSA) with 3-Satisfiability (3-SAT) logic to initiate an Artificial Intelligence (AI) model that executes optimization tasks for industrial data. The selection of 3-SAT logic is vital in data mining to represent entries of Amazon Employees Resources Access (AERA) via information theory. The proposed model employs CSA to improve the learning phase of DHNN by capitalizing features of CSA such as hypermutation and cloning process. This resulting the formation of the proposed model, as an alternative machine learning model to identify factors that should be prioritized in the approval of employees resources applications. Subsequently, reverse analysis method (SATRA) is integrated into our proposed model to extract the relationship of AERA entries based on logical representation. The study will be presented by implementing simulated, benchmark and AERA data sets with multiple performance evaluation metrics. Based on the findings, the proposed model outperformed the other existing methods in AERA data extraction.

When a local Hamiltonian must be frustration-free.

A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion-a sufficient condition-under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer's theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian's interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory.

Labelled Interpolation Systems for Hyper-Resolution, Clausal, and Local Proofs.

Craig's interpolation theorem has numerous applications in model checking, automated reasoning, and synthesis. There is a variety of interpolation systems which derive interpolants from refutation proofs; these systems are ad-hoc and rigid in the sense that they provide exactly one interpolant for a given proof. In previous work, we introduced a parametrised interpolation system which subsumes existing interpolation methods for propositional resolution proofs and enables the systematic variation of the logical strength and the elimination of non-essential variables in interpolants. In this paper, we generalise this system to propositional hyper-resolution proofs as well as clausal proofs. The latter are generated by contemporary SAT solvers. Finally, we show that, when applied to local (or split) proofs, our extension generalises two existing interpolation systems for first-order logic and relates them in logical strength.

Predicting the satisfiability of Boolean formulas by incorporating gated recurrent unit (GRU) in the Transformer framework.

The Boolean satisfiability (SAT) problem exhibits different structural features in various domains. Neural network models can be used as more generalized algorithms that can be learned to solve specific problems based on different domain data than traditional rule-based approaches. How to accurately identify these structural features is crucial for neural networks to solve the SAT problem. Currently, learning-based SAT solvers, whether they are end-to-end models or enhancements to traditional heuristic algorithms, have achieved significant progress. In this article, we propose TG-SAT, an end-to-end framework based on Transformer and gated recurrent neural network (GRU) for predicting the satisfiability of SAT problems. TG-SAT can learn the structural features of SAT problems in a weakly supervised environment. To capture the structural information of the SAT problem, we encodes a SAT problem as an undirected graph and integrates GRU into the Transformer structure to update the node embeddings. By computing cross-attention scores between literals and clauses, a weighted representation of nodes is obtained. The model is eventually trained as a classifier to predict the satisfiability of the SAT problem. Experimental results demonstrate that TG-SAT achieves a 2%-5% improvement in accuracy on random 3-SAT problems compared to NeuroSAT. It also outperforms in SR(N), especially in handling more complex SAT problems, where our model achieves higher prediction accuracy.

The Reasoning Engine: A Satisfiability Modulo Theories-Based Framework for Reasoning About Discrete Biological Models.

We present a framework called the Reasoning Engine, which implements Satisfiability Modulo Theories (SMT)-based methods within a unified computational environment to address diverse biological analysis problems. The Reasoning Engine was used to reproduce results from key scientific studies, as well as supporting new research in stem cell biology. The framework utilizes an intermediate language for encoding partially specified discrete dynamical systems, which bridges the gap between high-level domain-specific languages and low-level SMT solvers. We provide this framework as open source together with various biological case studies, illustrating the synthesis, enumeration, optimization, and reasoning over models consistent with experimental observations to reveal novel biological insights.

Deep Graph Learning for Circuit Deobfuscation.

Circuit obfuscation is a recently proposed defense mechanism to protect the intellectual property (IP) of digital integrated circuits (ICs) from reverse engineering. There have been effective schemes, such as satisfiability (SAT)-checking based attacks that can potentially decrypt obfuscated circuits, which is called deobfuscation. Deobfuscation runtime could be days or years, depending on the layouts of the obfuscated ICs. Hence, accurately pre-estimating the deobfuscation runtime within a reasonable amount of time is crucial for IC designers to optimize their defense. However, it is challenging due to (1) the complexity of graph-structured circuit; (2) the varying-size topology of obfuscated circuits; (3) requirement on efficiency for deobfuscation method. This study proposes a framework that predicts the deobfuscation runtime based on graph deep learning techniques to address the challenges mentioned above. A conjunctive normal form (CNF) bipartite graph is utilized to characterize the complexity of this SAT problem by analyzing the SAT attack method. Multi-order information of the graph matrix is designed to identify the essential features and reduce the computational cost. To overcome the difficulty in capturing the dynamic size of the CNF graph, an energy-based kernel is proposed to aggregate dynamic features into an identical vector space. Then, we designed a framework, Deep Survival Analysis with Graph (DSAG), which integrates energy-based layers and predicts runtime inspired by censored regression in survival analysis. Integrating uncensored data with censored data, the proposed model improves the standard regression significantly. DSAG is an end-to-end framework that can automatically extract the determinant features for deobfuscation runtime. Extensive experiments on benchmarks demonstrate its effectiveness and efficiency.

Fault detection and therapeutic intervention in gene regulatory networks using SAT solvers.

Random somatic mutations disrupt homeostasis of the cell resulting in various undesirable phenotypes including proliferation. One of the most important questions in systems medicine research is the therapeutic intervention design, which requires the knowledge of these mutations. A single or multiple mutations can occur in the diseases like cancer. These mutations have been successfully modeled as stuck-at faults in the Boolean network model of the underlying regulatory system. Identification of these fault types for multiple stuck-at faults is a non-trivial problem and requires some system theoretic introspection. This manuscript addresses the dual problem of the fault identification and the therapeutic intervention. Both the problems are mapped to the Boolean satisfiability (SAT) problem. The underlying problems are solved using a fast SAT solver. The synthetic and biological examples elucidate the effectiveness of the mapping.

Automated Formal Reasoning to Uncover Molecular Programs of Self-Renewal.

The Reasoning Engine for Interaction Networks (RE:IN) is a tool that was developed initially for the study of pluripotency in mouse embryonic stem cells. A set of critical factors that regulate the pluripotent state had been identified experimentally, but it was not known how these genes interacted to stabilize self-renewal or commit the cell to differentiation. The methodology encapsulated in RE:IN enabled the exploration of a space of possible network interaction models, allowing for uncertainty in whether individual interactions exist between the pluripotency factors. This concept of an "abstract" network was combined with automated reasoning that allows the user to eliminate models that are inconsistent with experimental observations. The tool generalizes beyond the study of stem cell decision-making, allowing for the study of interaction networks more broadly across biology.

Griffin: A Tool for Symbolic Inference of Synchronous Boolean Molecular Networks.

Boolean networks are important models of biochemical systems, located at the high end of the abstraction spectrum. A number of Boolean gene networks have been inferred following essentially the same method. Such a method first considers experimental data for a typically underdetermined "regulation" graph. Next, Boolean networks are inferred by using biological constraints to narrow the search space, such as a desired set of (fixed-point or cyclic) attractors. We describe Griffin, a computer tool enhancing this method. Griffin incorporates a number of well-established algorithms, such as Dubrova and Teslenko's algorithm for finding attractors in synchronous Boolean networks. In addition, a formal definition of regulation allows Griffin to employ "symbolic" techniques, able to represent both large sets of network states and Boolean constraints. We observe that when the set of attractors is required to be an exact set, prohibiting additional attractors, a naive Boolean coding of this constraint may be unfeasible. Such cases may be intractable even with symbolic methods, as the number of Boolean constraints may be astronomically large. To overcome this problem, we employ an Artificial Intelligence technique known as "clause learning" considerably increasing Griffin's scalability. Without clause learning only toy examples prohibiting additional attractors are solvable: only one out of seven queries reported here is answered. With clause learning, by contrast, all seven queries are answered. We illustrate Griffin with three case studies drawn from the Arabidopsis thaliana literature. Griffin is available at: http://turing.iimas.unam.mx/griffin.

Synthesizing and tuning stochastic chemical reaction networks with specified behaviours.

Methods from stochastic dynamical systems theory have been instrumental in understanding the behaviours of chemical reaction networks (CRNs) arising in natural systems. However, considerably less attention has been given to the inverse problem of synthesizing CRNs with a specified behaviour, which is important for the forward engineering of biological systems. Here, we present a method for generating discrete-state stochastic CRNs from functional specifications, which combines synthesis of reactions using satisfiability modulo theories and parameter optimization using Markov chain Monte Carlo. First, we identify candidate CRNs that have the possibility to produce correct computations for a given finite set of inputs. We then optimize the parameters of each CRN, using a combination of stochastic search techniques applied to the chemical master equation, to improve the probability of correct behaviour and rule out spurious solutions. In addition, we use techniques from continuous-time Markov chain theory to analyse the expected termination time for each CRN. We illustrate our approach by synthesizing CRNs for probabilistically computing majority, maximum and division, producing both known and previously unknown networks, including a novel CRN for probabilistically computing the maximum of two species. In future, synthesis techniques such as these could be used to automate the design of engineered biological circuits and chemical systems.

Algorithm for finding partitionings of hard variants of boolean satisfiability problem with application to inversion of some cryptographic functions.

In this paper we propose an approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance one can construct different partitionings, each of them is a set of simplified versions of the original SAT instance. The effectiveness of an arbitrary partitioning is determined by the total time of solving of all SAT instances from it. We suggest the approach, based on the Monte Carlo method, for estimating time of processing of an arbitrary partitioning. With each partitioning we associate a point in the special finite search space. The estimation of effectiveness of the particular partitioning is the value of predictive function in the corresponding point of this space. The problem of search for an effective partitioning can be formulated as a problem of optimization of the predictive function. We use metaheuristic algorithms (simulated annealing and tabu search) to move from point to point in the search space. In our computational experiments we found partitionings for SAT instances encoding problems of inversion of some cryptographic functions. Several of these SAT instances with realistic predicted solving time were successfully solved on a computing cluster and in the volunteer computing project SAT@home. The solving time agrees well with estimations obtained by the proposed method.

Automated Synthesis and Analysis of Switching Gene Regulatory Networks.

Studying the gene regulatory networks (GRNs) that govern how cells change into specific cell types with unique roles throughout development is an active area of experimental research. The fate specification process can be viewed as a biological program prescribing the system dynamics, governed by a network of genetic interactions. To investigate the possibility that GRNs are not fixed but rather change their topology, for example as cells progress through commitment, we introduce the concept of Switching Gene Regulatory Networks (SGRNs) to enable the modelling and analysis of network reconfiguration. We define the synthesis problem of constructing SGRNs that are guaranteed to satisfy a set of constraints representing experimental observations of cell behaviour. We propose a solution to this problem that employs methods based upon Satisfiability Modulo Theories (SMT) solvers, and evaluate the feasibility and scalability of our approach by considering a set of synthetic benchmarks exhibiting possible biological behaviour of cell development. We outline how our approach is applied to a more realistic biological system, by considering a simplified network involved in the processes of neuron maturation and fate specification in the mammalian cortex.

Discovering rare behaviours in stochastic differential equations using decision procedures: applications to a minimal cell cycle model.

Stochastic Differential Equation (SDE) models are used to describe the dynamics of complex systems with inherent randomness. The primary purpose of these models is to study rare but interesting or important behaviours, such as the formation of a tumour. Stochastic simulations are the most common means for estimating (or bounding) the probability of rare behaviours, but the cost of simulations increases with the rarity of events. To address this problem, we introduce a new algorithm specifically designed to quantify the likelihood of rare behaviours in SDE models. Our approach relies on temporal logics for specifying rare behaviours of interest, and on the ability of bit-vector decision procedures to reason exhaustively about fixed-precision arithmetic. We apply our algorithm to a minimal parameterised model of the cell cycle, and take Brownian noise into account while investigating the likelihood of irregularities in cell size and time between cell divisions.