Deterministic Machine Research Articles

Quantification of uncertainty in 3-D seismic interpretation: implications for deterministic and stochastic geomodeling and machine learning

Abstract. In recent years, uncertainty has been widely recognized in geosciences, leading to an increased need for its quantification. Predicting the subsurface is an especially uncertain effort, as our information either comes from spatially highly limited direct (1-D boreholes) or indirect 2-D and 3-D sources (e.g., seismic). And while uncertainty in seismic interpretation has been explored in 2-D, we currently lack both qualitative and quantitative understanding of how interpretational uncertainties of 3-D datasets are distributed. In this work, we analyze 78 seismic interpretations done by final-year undergraduate (BSc) students of a 3-D seismic dataset from the Gullfaks field located in the northern North Sea. The students used Petrel to interpret multiple (interlinked) faults and to pick the Base Cretaceous Unconformity and Top Ness horizon (part of the Middle Jurassic Brent Group). We have developed open-source Python tools to explore and visualize the spatial uncertainty of the students' fault stick interpretations, the subsequent variation in fault plane orientation and the uncertainty in fault network topology. The Top Ness horizon picks were used to analyze fault offset variations across the dataset and interpretations, with implications for fault throw. We investigate how this interpretational uncertainty interlinks with seismic data quality and the possible use of seismic data quality attributes as a proxy for interpretational uncertainty. Our work provides a first quantification of fault and horizon uncertainties in 3-D seismic interpretation, providing valuable insights into the influence of seismic image quality on 3-D interpretation, with implications for deterministic and stochastic geomodeling and machine learning.

An image encryption scheme based on hybridizing digital chaos and finite state machine

Image encryption protects visual information by transforming images into an incomprehensible form. Chaotic systems are used to design image ciphers due to properties such as ergodicity and initial condition sensitivity. A chaos-based cipher derives its security strength from its underlying digital chaotic map, thus a more complex map leads to higher security. This paper introduces an enhancement to a tent map’s chaotic properties by hybridizing it with a deterministic finite state machine. We denote the resulting digital one-dimensional chaotic system as TM-DFSM. Chaotic analyses indicate that the new chaotic system has higher nonlinearity, sensitivity to initial condition, and larger chaotic parameter range than other recently proposed one-dimensional chaotic systems. We then propose a new image encryption scheme based on TM-DFSM, capable of performing both confusion and diffusion operations in one pass while also having a flexible key space. The encryption operations are designed to achieve maximal confusion and diffusion properties. Changing a single bit of the plainimage or secret key will result in an entirely different cipherimage. The proposed cipher has been analyzed using histogram analysis, contrast analysis, local Shannon entropy, resistance against differential cryptanalysis, and key security. Performance comparison with other recent schemes also depicts the proposed cipher’s superiority.

$\mathcal k$-branching uio sequences for partially specified observable non-deterministic fsms

In black-box testing, test sequences may be constructed from systems modelled as deterministic finite-state machines (DFSMs) or, more generally, observable non-deterministic finite state machines (ONFSMs). Test sequences usually contain state identification sequences, with unique input output sequences ( <small>UIOs</small> ) often being used with DFSMs. This paper extends the notion of <small>UIOs</small> to ONFSMs. One challenge is that, as a result of non-determinism, the application of an input sequence can lead to exponentially many expected output sequences. To address this scalability problem, we introduce <inline-formula><tex-math notation="LaTeX">${\mathcal K}$</tex-math></inline-formula> - <small>UIOs</small> : <small>UIOs</small> that lead to at most <inline-formula><tex-math notation="LaTeX">${\mathcal K}$</tex-math></inline-formula> output sequences from states of <inline-formula><tex-math notation="LaTeX">$M$</tex-math></inline-formula> . We show that checking <inline-formula><tex-math notation="LaTeX">${\mathcal K}$</tex-math></inline-formula> - <small>UIO</small> existence is PSPACE-Complete if the problem is suitably bounded; otherwise it is in EXPSPACE and PSPACE-Hard. We provide a massively parallel algorithm for constructing <inline-formula><tex-math notation="LaTeX">${\mathcal K}$</tex-math></inline-formula> - <small>UIOs</small> and the results of experiments on randomly generated and real FSM specifications. The proposed algorithm was able to construct <small>UIOs</small> in cases where the existing <small>UIO</small> generation algorithm could not and was able to construct <small>UIOs</small> from FSMs with 38K states and 400K transitions.

AUTO STEMMING OF AZERBAIJANI LANGUAGE

One of important features in natural language processing is to find the root of a word. Stemming means to remove prefixes, suffixes, and infixes for finding the root of the word. Its aims are about to information retrieval, exploring text, machine for translation, and word look up based on its root. Stemming increases document retrieval by 10-50% in most of international languages, it also compresses the size of web-based table indexes documents up to 50%. In this paper, by analyzing stemming approaches, using structural methods, and deterministic finite automaton machine, applying 274 existing prefixes in language (linkage), a stemming system for Azerbaijani language is generated. Experimental result demonstrates that the proposed algorithm performs more than 97% accuracy.

Spatiotemporal Prediction of PM2.5 Concentrations at Different Time Granularities Using IDW-BLSTM

As air pollution becomes an increasing concern globally, governments, and research institutions have attached great importance to air quality prediction to help give early warnings and prevent the impacts of air pollution. The existing prediction methods for air quality forecasting include deterministic methods, statistical methods, machine learning, and deep learning methods. Deep learning-based prediction methods have attracted much attention these years due to its high performance and powerful modeling capability. However, the majority of the deep learning methods only focus on the prediction of the places where there have monitoring stations, and limited studies have integrated deep learning to predict places without monitoring stations. To address the limitations, this paper proposes a new methodology framework combining a deep learning network, namely, bi-directional long short-term memory (BLSTM) network and the inverse distance weighting (IDW) technique for the spatiotemporal predictions of air pollutants at different time granularities. The BLSTM can effectively capture the long-term temporal mechanism of air pollution. The IDW layer, on the other hand, can consider the spatial correlation of air pollution and interpolate the spatial distribution. A case study is conducted to validate the effectiveness of the proposed methodology. The PM2.5 concentration at Guangdong, China is forecasted. Prediction performances of the LSTM network at hourly, daily, and weekly granularities and over different time spans are presented. Spatial distribution of the predicted PM2.5 concentrations and the prediction errors are analyzed. The experimental results demonstrate that the proposed method can achieve better prediction performance for the PM2.5 concentration compared with other models.

Prediction of aerosol optical depth in West Asia using deterministic models and machine learning algorithms

Abstract Because of the lack of ground-based observations in large parts of West Asia, Aerosol Optical Depth (AOD) is mainly monitored by using remote sensing techniques. AOD can also be predicted by short term forecasts with commonly called Deterministic weather prediction models (DMs). The skill of DMs in reproducing remotely sensed observations when averaged over monthly time scales over West Asia is rather limited due to significant uncertainties in inputs and complexity of dust, which is the dominant type of aerosols in the region. Machine Learning Algorithms (MLAs), which require much less computational expenses than DMs, can be used. Using Moderate Resolution Imaging Spectroradiometer (MODIS) Deep Blue (DB) AOD as the representative of response variable, MLAs, especially Multivariate Adaptive Regression Splines (MARS) and Support Vector Machines (SVM), outperformed DMs on monthly time scale. MLAs have yielded lower prediction error (RMSE) and higher correlation with observations than DMs. In addition, findings disclosed that DMs, especially MACC, have failed to simulate observed AOD values over western Iran where the Zagros Mountains prevent advection of fine dust particles to the east of the study area. Prediction errors of MLAs and DMs along with major DB AOD peaks, over Iraq, can be traced back to the rough resolution of variable datasets, omission of some unknown influential predictors representing the life cycle of dust and/or other aerosols, and scarcity of extreme cases. It also remains to be tested in how far the results presented can be generalized to other regions and time scales.

Demand response scheduling in industrial asynchronous production lines constrained by available power and production rate

Energy efficiency in factories is a new paradigm arising with Demand Response (DR) programs that enables energy providers to ask their clients to reduce their power consumption for a given time. In this paper, we consider demand side management of an industrial customer who owns asynchronous production line systems. Our aim is to help the customer achieve a good trade-off between production rates and power consumption during DR events. To attain this objective, we develop a framework named DR-Mgmt to schedule activities of machines on production lines so that the number of simultaneously working machines is maximized while satisfying DR constraints. Our framework first models activities of a production line using a new approach based on temporal deterministic finite station machine concept, where each state represents machine status (working/idle) and transitions capture temporal changes. Then, the problem of finding an optimal schedule from all feasible schedules is handled by selecting the optimal set of state transitions. We adapt the well-known local search heuristic to find near-optimal transitions. Numerical results show a significant benefit of our approach on production rates during DR intervals. Compared to other approaches, the proposed framework performs best and improves production rates up to 70% in some cases with higher total power consumption. We also validate our work by a real case study.

Single-machine common due date total earliness/tardiness scheduling with machine unavailability

Research on non-regular performance measures is at best scarce in the deterministic machine scheduling literature with machine unavailability constraints. Moreover, almost all existing works in this area assume either that processing on jobs interrupted by an interval of machine unavailability may be resumed without any additional setup/processing or that all prior processing is lost. In this work, we intend to partially fill these gaps by studying the problem of scheduling a single machine so as to minimize the total deviation of the job completion times from an unrestrictive common due date when one or several fixed intervals of unavailability are present in the planning horizon. We also put serious effort into investigating models with semi-resumable jobs so that processing on a job interrupted by an interval of machine unavailability may later be resumed at the expense of some extra processing time. The conventional assumptions regarding resumability are also taken into account. Several interesting cases are identified and explored, depending on the resumability scheme and the location of the interval of machine unavailability with respect to the common due date. The focus of analysis is on structural properties and drawing the boundary between polynomially solvable and $$\mathcal {NP}$$ -complete cases. Pseudo-polynomial dynamic programming algorithms are devised for $$\mathcal {NP}$$ -complete variants in the ordinary sense.

A Class of 2-Head Finite Automata for Linear Languages

Both deterministic and non-deterministic nite state machines (automata) recognize regular languages exactly. Now we extend these machines using two heads to characterize even-linear and linear languages. The heads move in opposite directions in these automata. For even-linear languages, deterministic automata have the same eciency as non-deterministic ones, but for the general case (linear languages) only the non-deterministic version is sucient. We compare our automata to other two-head automata as well.

On store languages of language acceptors

It is well known that the “store language” of every pushdown automaton — the set of store configurations (state and stack contents) that can appear as an intermediate step in accepting computations — is a regular language. Here many models of language acceptors with various store structures are examined, along with a study of their store languages. For each model, an attempt is made to find the simplest model that accepts their store languages. Some connections between store languages of one-way and two-way machines are demonstrated, as with connections between nondeterministic and deterministic machines. A nice application of these store language results is also presented, showing a general technique for proving families accepted by many deterministic models are closed under right quotient with regular languages, resolving some open questions (and significantly simplifying proofs for others that are known) in the literature. Lower bounds on the space complexity of Turing machines for having non-regular store languages are obtained.

Towards robustness of response times: minimising the maximum inter-completion time on parallel machines

Motivated by scheduling practices that require a response to unplanned high-priority jobs as soon as possible without preempting any in-processing jobs, this paper considers a deterministic identical parallel machine scheduling problem to achieve robustness with regard to a worst-case response time. To the best of our knowledge, this paper is the first to study the objective of minimising the maximum inter-completion time, i.e. the maximum time difference between any two consecutive completion times of jobs. For this novel scheduling problem, we first show its NP-hardness, and then propose an integer linear programming formulation and three heuristic approaches. Numerical experiments demonstrate the efficiency of our solution methods.

Variations of checking stack automata: Obtaining unexpected decidability properties

We introduce a model of one-way language acceptors (a variant of a checking stack automaton) and show the following decidability properties:1.The deterministic version has a decidable membership problem but has an undecidable emptiness problem.2.The nondeterministic version has an undecidable membership problem and emptiness problem. There are many models of accepting devices for which there is no difference with these problems between deterministic and nondeterministic versions, i.e., the membership problem for both versions are either decidable or undecidable, and the same holds for the emptiness problem. As far as we know, the model we introduce above is the first one-way model to exhibit properties (1) and (2). We define another family of one-way acceptors where the nondeterministic version has an undecidable emptiness problem, but the deterministic version has a decidable emptiness problem. We also know of no other model with this property in the literature. We also investigate decidability properties of other variations of checking stack automata (e.g., allowing multiple stacks, two-way input, etc.). Surprisingly, two-way deterministic machines with multiple checking stacks and multiple reversal-bounded counters are shown to have a decidable membership problem, a very general model with this property.

Insertion operations on deterministic reversal-bounded counter machines

Several insertion operations are studied applied to languages accepted by one-way and two-way deterministic reversal-bounded multicounter machines. These operations are defined by the ideals obtained from relations such as the prefix, infix, suffix, and outfix relations, as well as operations defined from inverses of a type of deterministic transducer with reversal-bounded counters attached. The question of whether the resulting languages can always be accepted by deterministic machines with the same number (or larger number) of input-turns (resp., counters, counter-reversals, etc.) is investigated.

Adaptive distinguishing test cases of nondeterministic finite state machines: test case derivation and length estimation

Abstract A top-down approach is presented for checking the existence and derivation of an adaptive distinguishing test case (called also an adaptive distinguishing sequence) for a nondeterministic finite state machine (NDFSM). When such a test case exists, the method returns a canonical test case that includes all other distinguishing tests of the given complete observable NDFSM. In the second part of the paper, a constructive approach is provided for deriving a class of complete observable NDFSMs with n states, n &gt; 2, and 2 n − n − 1 inputs such that a shortest adaptive distinguishing test case for each NDFSM in the intended class has the length (height) 2 n − n − 1. In other words, we prove the reachability of the exponential upper bound on the length of a shortest adaptive distinguishing sequence for complete observable NDFSMs while for deterministic machines the upper bound is polynomial with respect to the number of states. For constructing the intended class of NDFSMs for a given n , we propose a special linear order over all the non-empty subsets without singletons of an n -element set. The obtained tight exponential upper bound initiates further research on identifying certain NDFSM classes where this upper bound is not reachable.

Compositional Analysis of Hybrid Systems Defined Over Finite Alphabets

We consider the stability and the input-output analysis problems of a class of large-scale hybrid systems composed of continuous dynamics coupled with discrete dynamics defined over finite alphabets, e.g., deterministic finite state machines (DFSMs). This class of hybrid systems can be used to model physical systems controlled by software. For such classes of systems, we use a method based on dissipativity theory for compositional analysis that allows us to study stability, passivity and input-output norms. We show that the certificates of the method based on dissipativity theory can be computed by solving a set of semi-definite programs. Nonetheless, the formulation based on semi-definite programs become computationally intractable for relatively large number of discrete and continuous states. We demonstrate that, for systems with large number of states consisting of an interconnection of smaller hybrid systems, accelerated alternating method of multipliers can be used to carry out the computations in a scalable and distributed manner. The proposed methodology is illustrated by an example of a system with 60 continuous states and 18 discrete states.

Mutation Clusters from Cancer Exome.

We apply our statistically deterministic machine learning/clustering algorithm *K-means (recently developed in https://ssrn.com/abstract=2908286) to 10,656 published exome samples for 32 cancer types. A majority of cancer types exhibit a mutation clustering structure. Our results are in-sample stable. They are also out-of-sample stable when applied to 1389 published genome samples across 14 cancer types. In contrast, we find in- and out-of-sample instabilities in cancer signatures extracted from exome samples via nonnegative matrix factorization (NMF), a computationally-costly and non-deterministic method. Extracting stable mutation structures from exome data could have important implications for speed and cost, which are critical for early-stage cancer diagnostics, such as novel blood-test methods currently in development.

Deletion operations on deterministic families of automata

It is shown that one-way deterministic reversal-bounded multicounter languages are closed under right quotient with languages from many language families; even those defined by nondeterministic machines such as the context-free languages. Also, it is shown that when starting with one-way deterministic machines with one counter that makes only one reversal, taking the left quotient with languages from many different language families — again including those defined by nondeterministic machines such as the context-free languages — yields only one-way deterministic reversal-bounded multicounter languages. These results are surprising given the nondeterministic nature of the deletion. However, if there are two more reversals on the counter, or a second 1-reversal-bounded counter, taking the left quotient (or even just the suffix operation) yields languages that can neither be accepted by deterministic reversal-bounded multi-counter machines, nor by 2-way deterministic machines with one reversal-bounded counter.

The complexity of checking the existence and derivation of adaptive synchronizing experiments for deterministic FSMs

In this paper, we address the problem of setting a deterministic Finite State Machine (FSM) to a designated initial state. Differently from other papers, we propose to use adaptive synchronizing sequences (test cases) for this purpose and show that for weakly-connected deterministic complete reduced FSMs the problem of checking the existence of an adaptive synchronizing sequence is in P. For partial deterministic reduced FSMs the problem is PSPACE-complete.

Information rate of some classes of non-regular languages: An automata-theoretic approach

We show that the information rate of the language accepted by a reversal-bounded deterministic counter machine is computable. For the nondeterministic case, we provide computable upper bounds. For the class of languages accepted by multi-tape deterministic finite automata, the information rate is computable as well.

More on Minimizing Finite Automata with Errors — Nondeterministic Machines

We continue our research on minimization problems and related problems for automata w.r.t. to different error profiles, now considering nondeterministic finite automata (NFAs) as inputs. Here the error profiles are almost-equivalence and E-equivalence. We show that the minimization problems and their underlying equivalence problems become PSPACE-complete in most cases. The obtained results nicely fit to the known ones on ordinary NFA minimization, and show a significant difference to the previously obtained results on deterministic finite state machines.