Input Head Research Articles

Language Acceptors with a Pushdown: Characterizations and Complexity

We study one-way nondeterministic pushdown automata ([Formula: see text]), optionally with reversal-bounded counters. Finite-turn pushdown automata are pushdown automata with a bound on the number of switches between pushing and popping. We give new characterizations for finite-turn pushdown automata, and for finite-turn pushdown automata augmented with reversal-bounded counters. The first is in terms of multi-tape nondeterministic finite automata ([Formula: see text]), and the second is in terms of multi-tape [Formula: see text] with reversal-bounded counters. We then use the characterizations to determine the complexity of the languages defined by these automata. In particular, we show that languages accepted by finite-turn [Formula: see text] augmented with reversal-bounded counters are in [Formula: see text]. For the non-finite-turn case, the languages are in [Formula: see text] and in [Formula: see text]. We also look at the space complexity of languages accepted by two-way machines. In particular, we show that every language accepted by a two-way [Formula: see text] with reversal-bounded counters that makes a polynomial (resp., exponential) number of input head reversals is in [Formula: see text] (resp., [Formula: see text]). This remains true if the pushdown can flip its contents a bounded number of times.

Predictive modelling and latent space exploration of steel profile overstrength factors using multi‐head autoencoder‐regressors

AbstractThis paper investigates the suitability and interpretability of a data‐driven deep learning algorithm for multi cross sectional overstrength factor prediction. For this purpose, we first compile datasets consisting of experiments from literature on the overstrength factor of circular, rectangular and square hollow sections as well as I‐ and H‐sections. We then propose a novel multi‐head encoder architecture consisting of three input heads (one head per section type represented by respective features), a shared embedding layer as well as a subsequent regression tail for predicting the overstrength factor. By construction, this multi‐head architecture simultaneously allows for (i) the exploration of the nonlinear embedding of different cross‐sectional profiles towards the overstrength factor within the shared layer, and (ii) a forward prediction of the overstrength factor given profile features. Our framework enables for the first time an exploration of cross‐section similarity w.r.t. the overstrength factor across multiple sections and hence provides new domain insights in bearing capacities of steel cross‐sections, a much wider data exploration, since the encoder‐regressor can serve as meta model predictor. We demonstrate the quality of the predictive capabilities of the model and gain new insights of the latent space of different steel sections w.r.t. the overstrength factor. Our proposed method can easily be transferred to other multi‐input problems of Scientific Machine Learning.

Input-Driven Double-Head Pushdown Automata

We introduce and study input-driven deterministic and nondeterministic double-head pushdown automata. A double-head pushdown automaton is a slight generalization of an ordinary pushdown automaton working with two input heads that move in opposite directions on the common input tape. In every step one head is moved and the automaton decides on acceptance if the heads meet. Demanding the automaton to work input-driven it is required that every input symbol uniquely defines the action on the pushdown store (push, pop, state change). Normally this is modeled by a partition of the input alphabet and is called a signature. Since our automaton model works with two heads either both heads respect the same signature or each head owes its own signature. This results in two variants of input-driven double-head pushdown automata. The induced language families on input-driven double-head pushdown automata are studied from the perspectives of their language describing capability, their closure properties, and decision problems.

Dual Head and Dual Attention in Deep Learning for End-to-End EEG Motor Imagery Classification

Event-Related Desynchronization (ERD) or Electroencephalogram (EEG) wavelet is essential for motor imagery (MI) classification and BMI (Brain–Machine Interface) application. However, it is difficult to recognize multiple tasks for non-trained subjects that are indispensable for the complexities of the task or the uncertainties in the environment. The subject-independent scenario, where an inter-subject trained model can be directly applied to new users without precalibration, is particularly desired. Therefore, this paper focuses on an effective attention mechanism which can be applied to a subject-independent set to learn EEG motor imagery features. Firstly, a custom form of sequence inputs with spatial and temporal dimensions is adopted for dual headed attention via deep convolution net (DHDANet). Secondly, DHDANet simultaneously learns temporal and spacial features. The features of spacial attention on each input head are divided into two parts for spatial attentional learning subsequently. The proposed model is validated based on the EEG-MI signals collected from 54 subjects in two sessions with 200 trials in each sessions. The classification of left and right hand motor imagery in this paper achieves an average accuracy of 75.52%, a significant improvement compared to state-of-the-art methods. In addition, the visualization of the frequency analysis method demonstrates that the temporal-convolution and spectral-attention is capable of identifying the ERD for EEG-MI. The proposed machine learning structure enables cross-session and cross-subject classification and makes significant progress in the BMI transfer learning problem.

Translations of Steinhausen's Publications Provide Insight Into Their Contributions to Peripheral Vestibular Neuroscience.

The quantitative relationship between angular head movement and semicircular canal function is most often referenced to the well-known torsion-pendulum model that predicts cupular displacement from input head acceleration. The foundation of this model can be traced back to Steinhausen's series of papers between 1927 and 1933 whereby he endeavored to document observations of cupular displacements that would directly infer movement of the endolymph resulting from angular rotation. He also was the first to establish the direct relationship between cupular displacement and compensatory eye movements. While the chronology of these findings, with their successes and pitfalls, are documented in Steinhausen's work, it reflects a fascinating journey that has been inaccessible to the non-German speaking community. Therefore, the present compilation of translations, with accompanying introduction and discussion, was undertaken to allow a larger component of the vestibular scientific community to gain insight into peripheral labyrinthine mechanics provided by this historical account.

Generalizations of Checking Stack Automata: Characterizations and Hierarchies

We examine different generalizations of checking stack automata by allowing multiple input heads and multiple stacks, and characterize their computing power in terms of two-way multi-head finite automata and space-bounded Turing machines. For various models, we obtain hierarchies in terms of their computing power. Our characterizations and hierarchies expand or tighten some previously known results. We also discuss some decidability questions and the space/time complexity of the models.

Head Pose Estimation through Keypoints Matching between Reconstructed 3D Face Model and 2D Image.

Mainstream methods treat head pose estimation as a supervised classification/regression problem, whose performance heavily depends on the accuracy of ground-truth labels of training data. However, it is rather difficult to obtain accurate head pose labels in practice, due to the lack of effective equipment and reasonable approaches for head pose labeling. In this paper, we propose a method which does not need to be trained with head pose labels, but matches the keypoints between a reconstructed 3D face model and the 2D input image, for head pose estimation. The proposed head pose estimation method consists of two components: the 3D face reconstruction and the 3D–2D matching keypoints. At the 3D face reconstruction phase, a personalized 3D face model is reconstructed from the input head image using convolutional neural networks, which are jointly optimized by an asymmetric Euclidean loss and a keypoint loss. At the 3D–2D keypoints matching phase, an iterative optimization algorithm is proposed to match the keypoints between the reconstructed 3D face model and the 2D input image efficiently under the constraint of perspective transformation. The proposed method is extensively evaluated on five widely used head pose estimation datasets, including Pointing’04, BIWI, AFLW2000, Multi-PIE, and Pandora. The experimental results demonstrate that the proposed method achieves excellent cross-dataset performance and surpasses most of the existing state-of-the-art approaches, with average MAEs of on Pointing’04, on BIWI, on AFLW2000, on Multi-PIE, and on Pandora, although the model of the proposed method is not trained on any of these five datasets.

Improving the robustness of the Comparison Model Method for the identification of hydraulic transmissivities

The Comparison Model Method (CMM) is a relatively simple and computationally efficient direct method for the identification of the transmissivity of a confined aquifer by solution of an inverse problem. However, it suffers some of the classical drawbacks related to ill-posedness and ill-conditioning of inverse methods. Effectiveness of the CMM can be improved by some approaches. First of all, the introduction of a factor which permits to limit the negative effects of small hydraulic gradients by selection of a single parameter of the algorithm. Moreover, the CMM can be cast in a tomographic framework, i.e., by profiting of multiple sets of data, corresponding to different flow situations, produced by different boundary conditions or sources terms. Numerical tests are performed on a synthetic aquifer, by means of an open-source implementation based on the use of flopy for the solution of the forward problems. The tests show that the above mentioned approaches improve the robustness of the CMM with respect to error on the input head data.

Decision problems and projection languages for restricted variants of two-dimensional automata

A two-dimensional automaton has a read-only input head that moves in four directions on a finite array of cells labeled by symbols of the input alphabet. A three-way two-dimensional automaton is prohibited from making upward moves, while a two-way two-dimensional automaton can only move downward and rightward.We show that the language emptiness problem for unary three-way nondeterministic two-dimensional automata is NP-complete, and is in P for general-alphabet two-way nondeterministic two-dimensional automata. We also show that the language equivalence and inclusion problems for two-way deterministic two-dimensional automata are decidable, while the language universality, equivalence, and inclusion problems for two-way nondeterministic two-dimensional automata are undecidable. The deterministic case is the first known positive decidability result for a language equivalence problem on two-dimensional automata over a general alphabet.Finally, we discuss the notion of row and column projection languages. We show that the row projection language of a unary three-way nondeterministic two-dimensional automaton is always regular, and that there exists a unary three-way deterministic two-dimensional automaton with a nonregular column projection language. For two-way nondeterministic two-dimensional automata, on the other hand, both the row and column projection languages are always regular.

Performance characteristics of a small water-hammer head pump

Abstract. Many rural farming areas are located far from a reliable electricity supply; hence, obtaining a reliable source of water for crops and livestock can prove to be an expensive venture. A water pump operating on the water-hammer effect requires no external power source and can serve as an effective means of pumping water to a higher altitude once a reliable supply is available. A low-cost small water-hammer head pump was designed to operate on the water-hammer head effect created by the sudden stoppage of a flowing fluid. This design consisted of an inlet section followed by the pump body, a pressure section and an outlet. The experimental set-up for testing the water-hammer head pump was designed with a variable head input and an adjustable head output. For each test configuration, a total of 10 samples of pump supply water and pump exhausted water were collected. The water samples were collected for 30 s in each case. The results showed a non-linear variation of water flow with respect to pump outlet height. The pump was capable of delivering water to a maximum height of 8 to 10 times the height of the input head. The pump operated at average efficiencies of 26 %, 16 % and 6 % when the delivery height was 2, 4 and 6 times the input head height, respectively. There was a 5 % incremental decrease in pump efficiency as the delivery height increased in increments of the corresponding input head height.

Properties of right one-way jumping finite automata

Right one-way jumping finite automata (ROWJFAs), were recently introduced in H. Chigahara et al. (2016) [3] and are jumping automata that process the input in a discontinuous way with the restriction that the input head reads deterministically from left-to-right starting from the leftmost letter in the input and when it reaches the end of the input word, it returns to the beginning and continues the computation. We characterize the family of permutation closed languages accepted by ROWJFAs in terms of Myhill-Nerode equivalence classes. Using this, we investigate closure and non-closure properties as well as inclusion relations to families of the Chomsky-hierarchy and related families. We also give more characterizations of languages accepted by ROWJFAs in the case that the language is given as the concatenation of two languages.

Unary Coded PSPACE-Complete Languages in ASPACE(loglog n)

We study the class of binary coded versions of unary languages that can be accepted by alternating machines with loglog n space. We show that there exists a binary PSpace-complete language $\mathcal {L}$ such that the unary coded version of $\mathcal {L}$ is in ASpace(loglog n). Consequently, the standard translation between unary languages accepted with loglog n space and binary languages accepted with log n space works for alternating machines if and only ifP = PSpace. In general, if a binary language is accepted deterministically in 2n⋅nO(1) time and, simultaneously, in nO(1) space—which covers many PSpace-complete problems—then its unary coded version is accepted by an alternating Turing machine using an initially delimited worktape of size loglog n. This unexpected power follows from the fact that, with an auxiliary worktape of size O(loglog n) on a unary input 1n, an alternating machine can simulate a stack with log n bits, representing the contents of the stack by its input head position. The standard push/pop operations on the stack are implemented by moving the head along the input.

Input-Driven Double-Head Pushdown Automata

We introduce and study input-driven deterministic and nondeterministic double-head pushdown automata. A double-head pushdown automaton is a slight generalization of an ordinary pushdown automaton working with two input heads that move in opposite directions on the common input tape. In every step one head is moved and the automaton decides on acceptance if the heads meet. Demanding the automaton to work input-driven it is required that every input symbol uniquely defines the action on the pushdown store (push, pop, state change). Normally this is modeled by a partition of the input alphabet and is called a signature. Since our automaton model works with two heads either both heads respect the same signature or each head owes its own signature. This results in two variants of input-driven double-head pushdown automata. The induced language families on input-driven double-head pushdown automata are studied from the perspectives of their language describing capability, their closure properties, and decision problems.

Characterization and complexity results on jumping finite automata

In a jumping finite automaton, the input head can jump to an arbitrary position within the remaining input after reading and consuming a symbol. We characterize the corresponding class of languages in terms of special shuffle expressions and survey other equivalent notions from the existing literature. Moreover, we present several results concerning computational hardness and algorithms for parsing and other basic tasks concerning jumping finite automata.

Two-way automata making choices only at the endmarkers

The question of the state-size cost for simulation of two-way nondeterministic automata (2nfas) by two-way deterministic automata (2dfas) was raised in 1978 and, despite many attempts, it is still open. Subsequently, the problem was attacked by restricting the power of 2dfas (e.g., using a restricted input head movement) to the degree for which it was already possible to derive some exponential gaps between the weaker model and the standard 2nfas. Here we use an opposite approach, increasing the power of 2dfas to the degree for which it is still possible to obtain a subexponential conversion from the stronger model to the standard 2dfas. In particular, it turns out that subexponential conversion is possible for two-way automata that make nondeterministic choices only when the input head scans one of the input tape endmarkers. However, there is no restriction on the input head movement. This implies that an exponential gap between 2nfas and 2dfas can be obtained only for unrestricted 2nfas using capabilities beyond the proposed new model.As an additional bonus, conversion into a machine for the complement of the original language is polynomial in this model. The same holds for making such machines self-verifying, halting, or unambiguous. Finally, any superpolynomial lower bound for the simulation of such machines by standard 2dfas would imply L≠NL. In the same way, the alternating version of these machines is related to L=?NL=?P, the classical computational complexity problems.

Nondeterminism is essential in small two-way finite automata with few reversals

On every n-long input, every two-way finite automaton (2fa) can reverse its input head O(n) times before halting. A 2fawith few reversals is an automaton where this number is only o(n). For every h, we exhibit a language that can be recognized by an h-state nondeterministic 2fa with few reversals, but requires Ω(2h) states on every deterministic 2fa with few reversals.

Superiority of one-way and realtime quantum machines

In automata theory, quantum computation has been widely examined for finite state machines, known as quantum finite automata (QFAs), and less attention has been given to QFAs augmented with counters or stacks. In this paper, we focus on such generalizations of QFAs where the input head operates in one-way or realtime mode, and present some new results regarding their superiority over their classical counterparts. Our first result is about the nondeterministic acceptance mode: Each quantum model architecturally intermediate between realtime finite state automaton and one-way pushdown automaton (one-way finite automaton, realtime and one-way finite automata with one-counter, and realtime pushdown automaton) is superior to its classical counterpart. The second and third results are about bounded error language recognition: for any k > 0, QFAs with k blind counters outperform their deterministic counterparts; and, a one-way QFA with a single head recognizes an infinite family of languages, which can be recognized by one-way probabilistic finite automata with at least two heads. Lastly, we compare the nondeterminictic and deterministic acceptance modes for classical finite automata with k blind counter(s), and we show that for any k > 0, the nondeterministic models outperform the deterministic ones.

On multi-head automata with restricted nondeterminism

In this work, we consider deterministic two-way multi-head automata, the input heads of which are nondeterministically initialised, i.e., in every computation each input head is initially located at some nondeterministically chosen position of the input word. This model serves as an instrument to investigate restricted nondeterminism of two-way multi-head automata. Our result is that, in terms of expressive power, two-way multi-head automata with nondeterminism in form of nondeterministically initialising the input heads or with restricted nondeterminism in the classical way, i.e., in every accepting computation the number of nondeterministic steps is bounded by a constant, do not yield an advantage over their completely deterministic counter-parts with the same number of input heads. We conclude this paper with a brief application of this result.

On synchronized multi-tape and multi-head automata

Motivated by applications to verification problems in string manipulating programs, we look at the problem of whether the heads in a multi-tape automaton are synchronized. Given an n-tape pushdown automaton M with a one-way read-only head per tape and a right end marker $ on each tape, and an integer k≥0, we say that M is k-synchronized if at any time during any computation of M on any input n-tuple (x1,…,xn) (whether or not it is accepted), no pair of input heads that are not on $ are more than k cells apart. This requirement is automatically satisfied if one of the heads has reached $. Note that an n-tuple (x1,…,xn) is accepted if M reaches the configuration where all n heads are on $ and M is in an accepting state. The automaton can be deterministic (DPDA) or nondeterministic (NPDA) and, in the special case, may not have a pushdown stack (DFA, NFA). We obtain decidability and undecidability results for these devices for both one-way and two-way versions. We also consider the notion of k-synchronized one-way and two-way multi-head automata and investigate similar problems.

Descriptional complexity of two-way pushdown automata with restricted head reversals

Two-way nondeterministic pushdown automata (2PDA) are classical nondeterministic pushdown automata (PDA) enhanced with two-way motion of the input head. In this paper, the subclass of 2PDA accepting bounded languages and making at most a constant number of input head turns is studied with respect to descriptional complexity aspects. In particular, the effect of reducing the number of pushdown reversals to a constant number is of interest. It turns out that this reduction leads to an exponential blow-up in case of nondeterministic devices, and to a doubly-exponential blow-up in case of deterministic devices. If the restriction on boundedness of the languages considered and on the finiteness of the number of head and pushdown turns is dropped, the resulting trade-offs are no longer bounded by recursive functions, and so-called non-recursive trade-offs are shown.