State Values Research Articles

Load balancing of multi-AGV road network based on improved Q-learning algorithm and macroscopic fundamental diagram

To address the challenges of traffic congestion and suboptimal operational efficiency in the context of large-scale applications like production plants and warehouses that utilize multiple automatic guided vehicles (multi-AGVs), this article proposed using an Improved Q-learning (IQL) algorithm and Macroscopic Fundamental Diagram (MFD) for the purposes of load balancing and congestion discrimination on road networks. Traditional Q-learning converges slowly, which is why we have proposed the use of an updated Q value of the previous iteration step as the maximum Q value of the next state to reduce the number of Q value comparisons and improve the algorithm’s convergence speed. When calculating the cost of AGV operation, the traditional Q-learning algorithm only considers the evaluation function of a single distance and introduces an improved reward and punishment mechanism to combine the operating distance of AGV and the road network load, which finally equalizes the road network load. MFD is the basic property of road networks and is based on MFD, which is combined with the Markov Chain (MC) model. Road network traffic congestion state discrimination method was proposed to classify the congestion state according to the detected number of vehicles on the road network. The MC model accurately discriminated the range near the critical point. Finally, the scale of the road network and the load factor were changed for several simulations. The findings indicated that the improved algorithm showed a notable ability to achieve equilibrium in the load distribution of the road network. This led to a substantial enhancement in AGV operational efficiency.

Specification Mining Based on the Ordering Points to Identify the Clustering Structure Clustering Algorithm and Model Checking

Software specifications are of great importance to improve the quality of software. To automatically mine specifications from software systems, some specification mining approaches based on finite-state automatons have been proposed. However, these approaches are inaccurate when dealing with large-scale systems. In order to improve the accuracy of mined specifications, we propose a specification mining approach based on the ordering points to identify the clustering structure clustering algorithm and model checking. In the approach, the neural network model is first used to produce the feature values of states in the traces of the program. Then, according to the feature values, finite-state automatons are generated based on the ordering points to identify the clustering structure clustering algorithm. Further, the finite-state automaton with the highest F-measure is selected. To improve the quality of the finite-state automatons, we refine it based on model checking. The proposed approach was implemented in a tool named MCLSM and experiments, including 13 target classes, were conducted to evaluate its effectiveness. The experimental results show that the average F-measure of finite-state automatons generated by our method reaches 92.19%, which is higher than most related tools.

The Non-Singular Terminal Sliding Mode Control of Underactuated Unmanned Surface Vessels Using Biologically Inspired Neural Network

Underactuated Unmanned Surface Vessels (USVs) are widely used in civil and military fields due to their small size and high flexibility, and trajectory tracking control is a critical research area for underactuated USVs. This paper proposes a trajectory tracking control strategy using the Biologically Inspired Neural Network (BINN) for USVs to improve tracking speed and accuracy. A virtual control law is designed to obtain the required virtual velocity for trajectory tracking control, in which the velocity error is calibrated to ensure that the position error converges to zero. To observe and compensate for unknown and complex environmental disturbances such as wind, waves, and currents, a nonlinear extended state observer (NESO) is designed. Then, a controller based on Non-singular Terminal Sliding Mode (NTSM) is designed to resolve the problems of singular value and controller chattering and to improve the controller response speed. A BINN is introduced to simplify the process of differentiation, reduce the input values of the initial state, and solve the problem of thruster input saturation. Finally, the Lyapunov stability theory is utilized to analyze the stability of the proposed algorithm. The simulation results show that the proposed algorithm has a higher trajectory tracking accuracy and speed than traditional methods.

A Machine Learning Algorithm That Experiences the Evolutionary Algorithm’s Predictions—An Application to Optimal Control

Using metaheuristics such as the Evolutionary Algorithm (EA) within control structures is a realistic approach for certain optimal control problems. They often predict the optimal control values over a prediction horizon using a process model (PM). The computational effort sometimes causes the execution time to exceed the sampling period. Our work addresses a new issue: whether a machine learning (ML) algorithm could “learn” the optimal behaviour of the couple (EA and PM). A positive answer is given by proposing datasets apprehending this couple’s optimal behaviour and appropriate ML models. Following a design procedure, a number of closed-loop simulations will provide the sequences of optimal control and state values, which are collected and aggregated in a data structure. For each sampling period, datasets are extracted from the aggregated data. The ML algorithm experiencing these datasets will produce a set of regression functions. Replacing the EA predictor with the ML model, new simulations are carried out, proving that the state evolution is almost identical. The execution time decreases drastically because the PM’s numerical integrations are totally avoided. The performance index equals the best-known value. In different case studies, the ML models succeeded in capturing the optimal behaviour of the couple (EA and PM) and yielded efficient controllers.

SYNTHESIS OF VHDL-MODEL OF A FINITE STATE MACHINE WITH DATAPATH OF TRANSITIONS

Context. The problem of building a program model of a finite state machine with datapath of transitions using VHDL language is considered. The model synthesis process is identified with the synthesis of this type of finite state machine, since the built model can be used both for the analysis of the device’s behavior and for the synthesis of its logic circuit in the FPGA basis. The object of the research is the automated synthesis of the logic circuit of the finite state machine with the datapath of transitions, based on the results of which numerical characteristics of the hardware expenses for the implementation of the state machine circuit can be obtained. This makes it possible to evaluate the effectiveness of using this structure of the finite state machine when implementing a given control algorithm.
 Objective. Development and research of a VHDL model of a finite state machine with datapath of transitions for the analysis of the behavior of the state machine and the quantitative assessment of hardware expenses in its logic circuit.
 Method. The research is based on the structural diagram of a finite state machine with datapath of transitions. The synthesis of individual blocks of the structure of the state machine is carried out according to a certain procedure by the given graph-scheme of the con-trol algorithm. It is proposed to present the result of the synthesis in the form of a VHDL description based on the fixed values of the states codes of the state machine. The process of synthesizing the datapath of transitions, the block of formation of codes of transitions operations and the block of formation of microoperations is demonstrated. VHDL description of that blocks is carried out in a synthesizable style, which allows synthesis of the logic circuit of the finite state machine based on FPGA with the help of modern CAD and obtaining numerical characteristics of the circuit, in particular, the value of hardware expenses. To analyze the correctness of the synthesized circuit, the process of developing the behavioral component of the VHDL model, the function of which is the generation of input signals of the finite state machine, is considered. The classical combination of the synthesizable and behavioral parts of the model allows presenting the results of the synthesis of a finite state machine with datapath of transitions as a separate project that can be used as a structural component of the designed digital system.
 Results. Using the example of an abstract graph-scheme of the control algorithm, a VHDL model of a finite state machine with datapath of transitions was developed. With the help of CAD AMD Vivado, a synthesis of the developed model was carried out and behavioral modeling of the operation of the finite state machine circuit was carried out. The results of the circuit synthesis made it possible to obtain the value of hardware expenses when implementing the circuit in the FPGA basis. According to the results of behavioral modeling, time diagrams were obtained, which testify to the correctness of the implementation of the functions of transitions and outputs of the synthesized state machine.
 Conclusions. In traditional VHDL models of finite state machines, the states do not contain specific codes and are identified using literals. This allows CAD to encode states at its own discretion. However, this approach is not suitable for describing a finite state machine with datapath of transitions. The transformation of states codes using a set of arithmetic and logic operations requires the use of fixed values of states codes, which determines the specifics of the VHDL model proposed in this paper. This and similar models can be used, in particular, in the study of the effectiveness of a finite state machine according to the criterion of hardware expenses in the device circuit.

A 3E analysis of a multi‐power generation system employing CO2, LNG, and Organic Rankine cycles

AbstractOne avenue in increasing the energy efficiency of energy systems is through utilizing the thermal energy of flue gases of industrial plants. On this thread, herein, a novel combined cascade cycle for heat recovery of flue gases of an industrial plant is proposed comprising of an organic Rankine cycle (ORC), high‐pressure transcritical CO2 cycle, transcritical CO2 cycle, and a liquefied natural gas (LNG) regasification cycle. System analysis is conducted using energy, exergy, and eco‐exergy equations. The optimization is carried out using the TOPSIS multi‐objective method. Exergy efficiency, net output work, and cost are identified as the optimization objectives. The optimization process focused on fine‐tuning variables including the vapor generator pinch point temperature, ORC turbine inlet pressure, ORC condenser pressure, and ORC condenser pinch point temperature, with optimal values gauged at 19.31°C, 29.59 bar, 1.413 bar, and 14.52°C, respectively. The preheater had the largest exergy destruction share, followed by the heat exchanger unit. The analysis showed that the ORC condenser pressure and temperature difference between two working fluids in the heat exchanger were the most critical parameters in the proposed cycle, significantly affecting the system performance. Accordingly, the exergy efficiency, net output work, and cost values in the optimal state were equal to 15.2%, 6416 kW, and 0.7457 $/s, respectively. The advantages of the proposed system include efficient heat recovery through the coupling of the multiple cycles and enhanced energy conversion pertinent to a wider range of temperatures, maximizing the overall energy extraction from the waste heat.

Identifying epigenetic aging moderators using the epigenetic pacemaker.

Epigenetic clocks are DNA methylation-based chronological age prediction models that are commonly employed to study age-related biology. The difference between the predicted and observed age is often interpreted as a form of biological age acceleration, and many studies have measured the impact of environmental and disease-associated factors on epigenetic age. Most epigenetic clocks are fit using approaches that minimize the error between the predicted and observed chronological age, and as a result, they may not accurately model the impact of factors that moderate the relationship between the actual and epigenetic age. Here, we compare epigenetic clocks that are constructed using penalized regression methods to an evolutionary framework of epigenetic aging with the epigenetic pacemaker (EPM), which directly models DNA methylation as a function of a time-dependent epigenetic state. In simulations, we show that the value of the epigenetic state is impacted by factors such as age, sex, and cell-type composition. Next, in a dataset aggregated from previous studies, we show that the epigenetic state is also moderated by sex and the cell type. Finally, we demonstrate that the epigenetic state is also moderated by toxins in a study on polybrominated biphenyl exposure. Thus, we find that the pacemaker provides a robust framework for the study of factors that impact epigenetic age acceleration and that the effect of these factors may be obscured in traditional clocks based on linear regression models.

Self-Insuring against Liability Risk: Evidence from Physicians’ Home Values in States with Unlimited Homestead Exemptions

Self-Insuring against Liability Risk: Evidence from Physicians’ Home Values in States with Unlimited Homestead Exemptions

Aging and confinement in subordinated fractional Brownian motion

We study the effects of aging properties of subordinated fractional Brownian motion (FBM) with drift and in harmonic confinement, when the measurement of the stochastic process starts a time ta > 0 after its original initiation at t = 0. Specifically, we consider the aged versions of the ensemble mean squared displacement (MSD) and the time averaged MSD (TAMSD). The aging subordinated FBM exhibits a disparity between MSD and TAMSD and is thus weakly nonergodic, while strong aging is shown to effect a convergence of the MSD and TAMSD. At long times, the MSD in the harmonic potential has a stationary value, that depends on the Hurst index of the parental (non-equilibrium) FBM. The TAMSD of confined subordinated FBM does not relax to a stationary value but increases sublinearly with lag time, analogously to confined CTRW. Interestingly, for the confined subordinated FBM, small aging time ta has no effect on the aged MSD, while at large aging time the aged MSD has monotonic increase ultimately with a power-law and is identical to the aged TAMSD.

D2CFR: Minimize Counterfactual Regret With Deep Dueling Neural Network.

Counterfactual regret minimization (CFR) is a popular method for finding approximate Nash equilibrium in two-player zero-sum games with imperfect information. Solving large-scale games with CFR needs a combination of abstraction techniques and certain expert knowledge, which constrains its scalability. Recent neural-based CFR methods mitigate the need for abstraction and expert knowledge by training an efficient network to directly obtain counterfactual regret without abstraction. However, these methods only consider estimating regret values for individual actions, neglecting the evaluation of state values, which are significant for decision-making. In this article, we introduce deep dueling CFR (D2CFR), which emphasizes the state value estimation by employing a novel value network with a dueling structure. Moreover, a rectification module based on a time-shifted Monte Carlo simulation is designed to rectify the inaccurate state value estimation. Extensive experimental results are conducted to show that D2CFR converges faster and outperforms comparison methods on test games.

Computer Go Research Based on Variable Scale Training and PUB-PMCTS

The mainstream Go AI algorithms represented by AlphaZero and KataGo suffer from low-quality samples in the early training period and low exploration efficiency when performing traditional Monte Carlo Tree Search (MCTS). For the shortcomings mentioned above: The variable scale training is proposed, i.e., introducing a variable scale board with boundary conditions of randomly placed stones at the boundary periphery, to pre-train a small-scale network for recommending local move strategy and ownership. This network is used to improve the backbone network’s moving policy and state value, enhancing the quality of game samples in the early stages of training. To improve the efficiency and convergence speed of the search, we propose the Parallel Monte Carlo Tree Search with Potential-Upper-Bound (PUB-PMCTS), i.e., executing multiple unevaluated searches sequentially and then evaluating multiple leaf nodes in parallel; also, the variance of the node’s action values are used to forecast the potential upper limit of the node. In addition, we add a self-attention mechanism in the network to extract global context information of features and add maximum entropy loss to grow the exploration ability of the model. With the improvements described above, the bot TransGo is designed. Experimental results show that in a 13×13 Go environment, TransGo has more stable performance and higher game level in the early training period compared with other algorithms. After four days of training with TransGo, KataGo, and AlphaZero: TransGo improved by 102 Elo compared to KataGo and over 1000 Elo compared to AlphaZero.

Theoretical study on the H-atom abstraction reactions of pentanol + HȮ2, part I: five branched pentanol isomers.

The chemical kinetic studies of hydrogen atom (H-atom) abstraction reactions by hydroperoxyl (HȮ2) radicals from five branched pentanol isomers, including 3-methyl-1-butanol, 2-methyl-1-butanol, 1,1-dimethyl-1-propanol, 1,2-dimethyl-1-propanol, and 2,2-dimethyl-1-propanol were investigated systematically through high-level ab initio calculations. Geometry optimization, frequency analysis, and zero-point energy (ZPE) corrections were performed for six reactants, twenty-three transition states (TSs), and twenty-four products at the M06-2X/6-311++G(d,p) level of theory. The intrinsic reaction coordinate calculation was performed at the same level of theory to confirm the transition state connection. The one-dimensional hindered rotor treatment for low-frequency torsional modes was also treated at the M06-2X/6-311++G(d,p) level of theory. The QCISD(T)/CBS level of theory was used to calculate the single-point energies for the species whose T1 diagnostic value was lower than 0.035. At the same time, the CASPT2/CBS level of theory was used to calculate the single-point energies for the channel in which the T1 diagnostic value of transition states was greater than 0.035. Rate constants for the H-atom abstraction reactions from the five branched pentanol isomers by HȮ2 radicals were calculated by using conventional transition state theory with asymmetric Eckart tunneling corrections in the temperature range of 500-2000 K. Rate constants and branching ratios for the title reactions and the rate rules for ten different H-atom abstraction types were investigated. Temperature-dependent thermochemistry properties for all reactants and products were calculated by the composite methods of G3/G4/CBS-QB3/CBS-APNO, which were in good agreement with the data available in the literature. Rate constants for the H-atom abstraction reactions by HȮ2 radical from branched pentanol isomers were investigated in this work as part I, and those for linear pentanol isomers will be analyzed in part II. All the calculated kinetics and thermochemistry data can be utilized in the model development for branched pentanol isomers oxidation.

Structural stability and electronic properties of charged point defects in monolayer blue phosphorus

As a new two-dimensional material, blue phosphorus has attracted considerable research interest due to its high carrier mobility and large bandgap. Although the structural defects of blue phosphorus have been discussed recently, the charged properties of these defects have not been explored. In this paper, using first-principles calculations based on density functional theory, the six most stable point defects and their corresponding charged states in blue phosphorus are studied, including Stone Wales (SW), single vacancy (SV), two double-vacancy (DV-1 and DV-2) and two substitution defects (O<sub>P</sub> and C<sub>P</sub>). The converged ionization energy values of charged defects in blue phosphorus are obtained by extrapolating the asymptotic expression of the energy dependent on the cell size. Subsequently, the formation energy values for different charge states are modified to determine their structural stabilities. Finally, their electronic properties are analyzed through band structures. The results suggest that SV<sup>1–</sup> is easy to ionize, owing to its lowest ionization energy (1.08 eV). Furthermore, among the defects we are considering, O<sub>P</sub><sup>1–</sup> is the most stable charged defect in blue phosphorus, with the lowest formation energy (–9.33 eV) under O-rich chemical potential condition. The negative formation energy indicates that O atoms can exist stably in blue phosphorus, implying that blue phosphorus is easily oxidized. The introduction of defect states will affect the bandgap of blue phosphorus, and the ionization of defects will cause the defect energy levels to shift, leading defects to transition between shallow and deep levels. This study provides theoretical guidance for the application of defect engineering in two-dimensional materials.

ХУДОЖНИК И ПЕДАГОГ А.Г. ПЕСИГИН: СТРАНИЦЫ ЖИЗНИ И ТВОРЧЕСТВА

The article is devoted to the life and work of the outstanding artist, writer and teacher Anatoly Georgievich Pesigin, who made a great contribution to the development of Russian art in the second half of the 20th century. During this rather difficult historical period for our country, culture faced an important task, which was to continue the formation and dissemination of new values of the Soviet state. In many ways, the solution of this issue was facilitated, among other things, by the creative activity of the portrait painter A.G. Pesigin. The creative path and stages of development of creative ideas, means of expression and themes of works in the process of searching for an individual language are consid ered. An example and characteristics of works from the initial period of creativity, brought up by the traditions of the academic school of the Penza Art School, are given. As well as the turning point and transformation of the creative method during the “thaw” period. The period of creation of graphic works in a characteristic linear manner in the process of illustrating books of Samara poets and writers is studied separately. In addition, the special pedagogical activity of Anatoly Georgievich was noted in educating young artists, effective forms and methods of working with students aimed at developing their creative abilities and desire to understand the world.

Effects of radiative heat loss on extinction limits of counterflow premixed ammonia-air flames

The effect of radiative heat loss on counterflow premixed ammonia-air flames has been investigated as a function of equivalence ratio and system pressure. Non-adiabatic counterflow premixed flame simulations incorporating detailed chemistry, transport, and radiative heat transfer in the optically thin limit have been employed to elucidate important underlying physics and extinction characteristics. Similar to methane-air flame systems, non-adiabatic counterflow premixed computations show that the combined effects of positive flame stretch, sub-unity Lewis number, and radiative heat loss lead to the extension of the lean flammability limit for ammonia-air flames, revealing a C-shaped curve near the lean flammability limit that exhibits both radiation-induced and stretch-induced extinction states. The computations compare favorably with the experimentally determined extinction stretch rate values for the stretch-induced extinction states over a wide range of equivalence ratios at different pressures up to 5 atm. A novel feature sensitivity analysis has also been developed to highlight important sensitive reactions for the stretch- and radiation-induced extinction states. Furthermore, the controlling chemistry at the dual-extinction states and at varying pressures are compared and discussed.

Guided Cooperation in Hierarchical Reinforcement Learning via Model-Based Rollout.

Goal-conditioned hierarchical reinforcement learning (HRL) presents a promising approach for enabling effective exploration in complex, long-horizon reinforcement learning (RL) tasks through temporal abstraction. Empirically, heightened interlevel communication and coordination can induce more stable and robust policy improvement in hierarchical systems. Yet, most existing goal-conditioned HRL algorithms have primarily focused on the subgoal discovery, neglecting interlevel cooperation. Here, we propose a novel goal-conditioned HRL framework named Guided Cooperation via Model-Based Rollout (GCMR; code is available at https://github.com/HaoranWang-TJ/GCMR_ACLG_official), aiming to bridge interlayer information synchronization and cooperation by exploiting forward dynamics. First, the GCMR mitigates the state-transition error within off-policy correction via model-based rollout, thereby enhancing sample efficiency. Second, to prevent disruption by the unseen subgoals and states, lower level Q -function gradients are constrained using a gradient penalty with a model-inferred upper bound, leading to a more stable behavioral policy conducive to effective exploration. Third, we propose a one-step rollout-based planning, using higher level critics to guide the lower level policy. Specifically, we estimate the value of future states of the lower level policy using the higher level critic function, thereby transmitting global task information downward to avoid local pitfalls. These three critical components in GCMR are expected to facilitate interlevel cooperation significantly. Experimental results demonstrate that incorporating the proposed GCMR framework with a disentangled variant of hierarchical reinforcement learning guided by landmarks (HIGL), namely, adjacency constraint and landmark-guided planning (ACLG), yields more stable and robust policy improvement compared with various baselines and significantly outperforms previous state-of-the-art (SOTA) algorithms.

Effect of Social Innovation and Social Value on Poverty Alleviation in Zamfara State

This study examined the effect of social innovation and social value on poverty alleviation in Zamfara state. The major objective of the study is to assess the relationship between social innovation and social value on poverty alleviation in Zamfara state. A survey method of study was adopted. Data was collected through a closed ended questionnaires which was design in a five linker scale. The data was analyzed using SMART –PLS3 model and the hypotheses were tested using bootstrapping model to run the analysis. The researchers anchored the study on Schumpeterian Theory of Innovation and Social Action Theory. The study revealed that there is a strong, positive, and statistically significant relationship between social innovation and poverty alleviation in Zamfara state. And it equally revealed that there is a negative and statistically significant relationship between social value and poverty alleviation in Zamfara state. Therefore the researchers recommended that organizations and policymakers should focus on creating enabling environment for social innovation to strive for better poverty alleviation in Zamfara state.

Multi-omics analysis of innate and adaptive responses to BCG vaccination reveals epigenetic cell states that predict trained immunity

Immune responses are tightly regulated yet highly variable between individuals. To investigate human population variation of trained immunity, we immunized healthy individuals with Bacillus Calmette-Guérin (BCG). This live-attenuated vaccine induces not only an adaptive immune response against tuberculosis but also triggers innate immune activation and memory that are indicative of trained immunity. We established personal immune profiles and chromatin accessibility maps over a 90-day time course of BCG vaccination in 323 individuals. Our analysis uncovered genetic and epigenetic predictors of baseline immunity and immune response. BCG vaccination enhanced the innate immune response specifically in individuals with a dormant immune state at baseline, rather than providing a general boost of innate immunity. This study advances our understanding of BCG's heterologous immune-stimulatory effects and trained immunity in humans. Furthermore, it highlights the value of epigenetic cell states for connecting immune function with genotype and the environment.

WHY QUALITY OF THE TEACHER MATTERS? TEACHERS AND TEACHING STYLE 

This article explores the teachers and their careers, and it aims to highlight the importance of the teachers’ quality, the way skilled teachers inspire and motivate their students by bringing life to curriculum. This article also emphasizes the importance of teaching skills. To accomplish our aim, the following task have been set: to experimentally study the teaching style of teachers and their ability to inspire students taking into consideration their values of priority, psycho-emotional state, self-assessment, teaching style and reliability of the facts. In order to achieve our goal, we used the test method to determine teachers’ teaching style. The main goal is to acknowledge the teaching style of teachers and their ability to inspire their students and mainly to discover how their methods affect the researcher's motivation and academic progress. As a result, we found out that the student’s motivation, learning improvements and academic achievements depend on the quality of the teacher. The motivation of a student in the third millennium requires a passionate and motivated teacher, who possesses a strategic vision within the education system and implements effective lesson plans.

Wavefunction theory and density functional theory analysis of ground and excited electronic states of TaB and WB.

Several low-lying electronic states of TaB and WB molecules were studied using ab initio multireference configuration interaction (MRCI), Davidson corrected MRCI (MRCI+Q), and coupled cluster singles doubles and perturbative triples [CCSD(T)] methods. Their full potential energy curves (PECs), equilibrium electron configurations, equilibrium bond distances (res), dissociation energies (Des), excitation energies (Tes), harmonic vibrational frequencies (ωes), and anharmonicities (ωexes) are reported. The MRCI dipole moment curves (DMCs) of the first 5 electronic states of both TaB and WB are also reported and the equilibrium dipole moment (μ) values are compared with the CCSD(T) μ values. The most stable 13Π (1σ22σ23σ11π3) and 15Δ (1σ22σ23σ11π21δ1) electronic states of TaB lie close in energy with ∼62 kcal mol-1De with respect to the Ta(4F) + B(2P) asymptote. However, spin-orbit coupling effects make the 15Δ0+ state the true ground state of TaB. The ground electronic state of WB (16Π) has the 1σ22σ13σ11π31δ2 electron configuration and is followed by the excited 16Σ+ and 14Δ states. Finally, the MRCI De, re, ωe, and ωexe values of the 13Π state of TaB and 16Π and 14Δ states of WB are used to assess the density functional theory (DFT) errors on a series of exchange-correlation functionals that span multiple-rungs of the Jacob's ladder of density functional approximations (DFA).