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The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined, even if it does not have a purely mathematical definition—and even if (as many have asserted) for that reason, the Church–Turing thesis (that the effectively calculable functions on natural numbers are exactly the general recursive functions), cannot be proved. However, it is logically provable from the notion of an effective procedure, without reliance on any (partially) mathematical thesis or conjecture concerning effective procedures, such as the Church–Turing thesis, that the class of effective procedures is undecidable, i.e., that there is no effective procedure for ascertaining whether a given procedure is effective. The proof does not even appeal to a precise definition of ‘effective procedure’. Instead, it relies solely and entirely on a basic grasp of the intuitive notion of such a procedure. Though the result itself is not surprising, it is also not without significance. It has the consequence, for example, that the solution to a decision problem, if it is to be complete, must be accompanied by a separate argument that the proposed ascertainment procedure is, in fact, a decision procedure, i.e., effective—for example, that it invariably terminates with the correct verdict.

Decision problems in physics have been an active field of research for quite a few decades resulting in some interesting findings in recent years. However, such research investigations are based on a priori knowledge of theoretical computer science and the technical jargon of set theory. Here, I discuss a particular, but a significant, instance of how decision problems in physics can be realised without such specific prerequisites. I expose a hitherto unnoticed contradiction, that can be posed as as decision problem, concerning the oil drop experiment, thereby resolve it by refining the notion of 'existence' in physics. This consequently leads to the undecidability of the charge spectral gap through the notion of 'undecidable charges' which is in tandem with the completeness condition of a theory as was stated by Einstein, Podolsky and Rosen in their seminal work. Decision problems can now be realised in connection with basic physics, in general, rather than quantum physics, in particular, as per some recent claims. [ABSTRACT FROM AUTHOR]

We address the decision problem for sentences involving univariate functions constructed from a fixed Pfaffian function of order 1. We present a new symbolic procedure solving this problem with a computable complexity based on the computation of suitable Sturm sequences. For a general Pfaffian function, we assume the existence of an oracle to determine the sign that a function of the class takes at a real algebraic number. As a by-product, we obtain a new oracle-free effective algorithm solving the same problem for univariate E-polynomials based on techniques that are simpler than the previous ones, and we apply it to solve a similar decision problem in the multivariate setting. Finally, we introduce a notion of Thom encoding for zeros of an E-polynomial and describe an algorithm for their computation. [ABSTRACT FROM AUTHOR]

We consider a natural generalization of the concept of order of an element in a group G : an element g ∈ G is said to have order k in a subgroup H (respectively, in a coset H u) of G if k is the first strictly positive integer such that g k ∈ H (respectively, g k ∈ H u). We study this notion and its algorithmic properties in the realm of free groups and some related families. Both positive and negative (algorithmic) results emerge in this setting. On the positive side, among other results, we prove that the order of elements, the set of orders (called spectrum), and the set of preorders (i.e. the set of elements of a given order) with respect to finitely generated subgroups are always computable in free and free times free-abelian groups. On the negative side, we provide examples of groups and subgroups having essentially any subset of natural numbers as relative spectrum; in particular, non-recursive and even not computably enumerable sets of natural numbers. Also, we take advantage of Mikhailova's construction to see that the spectrum membership problem is unsolvable for direct products of nonabelian free groups. [ABSTRACT FROM AUTHOR]

Maxwell's verbal statement of Coulomb's experimental verification of his hypothesis, concerning force between two electrified bodies, is suggestive of a modification of the respective computable expression on logical grounds. This modification is in tandem with the completeness condition for a physical theory, that was stated by Einstein, Podolsky and Rosen in their seminal work. Working with such a modification, I show that the first Maxwell's equation, symbolically identifiable as ∇ · E = ρ / ϵ 0 from the standard literature, is unprovable. This renders Poynting's theorem to be unprovable as well. Therefore, the explanation of 'light' as 'propagation of electromagnetic energy' comes into question on theoretical grounds. [ABSTRACT FROM AUTHOR]

One of the main missions of a certain company is to predict its future for reasons of continuity, which reflect the balance of its long term, in various aspects. In this work, we propose the use of Markov Interval Chain models to help business leaders to make better decisions. The proposed model consists in considering the numbers of customers declared by each company, which are discrete values as centers of symmetric intervals. By this, we have avoided the problem of increase and decrease in the number of customers for each company. As an example, we applied this model to predict the distribution of market shares in the later period as a probability distribution intervals, which provides information's for companies to make decisions, and it gave satisfactory results. [ABSTRACT FROM AUTHOR]

Multi-attribute decision-making (MADM) refers to making preference decisions via assessing a finite number of pre-specified alternatives under multiple and usually conflicting attributes. Many problems in the field of additive manufacturing (AM) are essentially MADM problems or can be converted into MADM problems. Recently, a variety of MADM methods have been applied to solve MADM problems in AM. This generates a series of interesting questions: What is the general trend of this research topic from the perspective of published articles every year? Which journals published the most articles on the research topic? Which articles on the research topic are the most cited? What MADM methods have been applied to the field of AM? What are the main strengths and weaknesses of each MADM method used? Which MADM method is the most used one in this field? What specific problems in AM have been tackled via using MADM methods? What are the main issues in existing MADM methods for AM that need to be addressed in future studies? To approach these questions, a review of MADM methods in AM is presented in this paper. Firstly, an overview of existing MADM methods in AM was carried out based on the perspective of specific MADM methods. A statistical analysis of these methods is then made from the aspects of published journal articles, applied specific methods, and solved AM problems. After that, the main issues in the application of MADM methods to AM are discussed. Finally, the research findings of this review are summarised. [ABSTRACT FROM AUTHOR]

Energy is recognised as an important indicator of economic development in a globalising world and is of vital importance to countries. In order to ensure sustainable development in a society, it is necessary to have abundant energy resources. These energy resources must be obtained at a reasonable cost and used for all the needs of society without causing any negative social impact. Power plants are recognized as the heart of the electricity generation industry in all countries with continuous operation. They are believed to have a critical and decisive role in the survival of industry and the economy. Therefore, they are certainly one of the most important pillars of development in a country. For this purpose, the selection of terrestrial renewable energy plants has been made in this study. Nowadays, the rapid increase in the world's population and industrialisation increase the need for energy. Energy needs are generally supplied from fossil fuel sources. Due to the decrease in fossil fuel resources in our country and in the world and the damage they cause to the environment, the importance of renewable energy sources has increased. The selection of energy sources is seen as a multi-criteria group decision making problem since alternatives (energy sources) are evaluated by multiple decision makers according to criteria. In this study, terrestrial renewable energy plants are ranked using the intuitionistic fuzzy WASPAS approach. Economic, environmental, technical, and social criteria are taken into account when determining the best terrestrial renewable energy plants for Turkey. As a result of the modelling, solar power plants are determined as the most suitable renewable energy source. [ABSTRACT FROM AUTHOR]

The issue of decision-making in an international negotiation is always one of the concerns of statesmen, officials and diplomats, because the wrong decision of a diplomat leads to failure in the negotiation. Game theory, which has attracted the attention of experts in various sciences, including political science, tries to make the best decisions in the decision-making and policy-making cycle on major issues to make decisions more rational and useful. In particular, the negotiations that are taking place today in the field of international relations can be examined on the basis of game theory and an agreement can be reached. In this research, we simulate the general process of a negotiation between the two countries with the help of game theory. Simply put, we simulate the actual process of a negotiation using a set of mathematical methods, models, and tools. In this regard, we classify negotiation into four stages: preparation for negotiation, exchange of proposals, reaching an agreement, and ending the negotiation. We model the preparation phase for the negotiation using finite game models and provide algebraic methods for calculating dominant performance and Nash equilibrium. According to the results of the first step, we model the exchange of suggestions with the help of dynamic game tree model. In the third stage, by solving tree models with the backward induction, we obtain the optimal strategies of the players. At the end of the negotiation, we will examine the conditions for reaching an agreement. Finally, a decision-making process in a negotiation is presented.

We review some simulation‐based methods to implement optimal decisions in sequential design problems as they naturally arise in clinical trial design. As a motivating example we use a stylized version of a dose‐ranging design in the ASTIN trial. The approach can be characterized as constrained backward induction. The nature of the constraint is a restriction of the decisions to a set of actions that are functions of the current history only implicitly through a low‐dimensional summary statistic. In addition, the action set is restricted to time‐invariant policies. Time‐dependence is only introduced indirectly through the change of the chosen summary statistic over time. This restriction allows computationally efficient solutions to the sequential decision problem. A further simplification is achieved by restricting optimal actions to be described by decision boundaries on the space of such summary statistics. [ABSTRACT FROM AUTHOR]

The problem of choosing the way to move people is often encountered both in scientific research and in everyday life. The difficulty of this process depends on the availability of many variants and the pursuit of satisfying transport needs at the minimum cost, in the shortest possible time and in the most comfortable conditions. The publication presents a decision problem of choosing the best transport option using multi-criteria methods. At the beginning authors present-ed the widely used methods of solving decision problems in the literature. Subsequently, based on the example of the Warsaw-Wroclaw connection, the MAJA multi-criteria assessment method algorithm was analysed. Both road, rail and air transport options were considered. Six possible variants of solutions were indicated, which were assessed in three sub-criteria: cost, time and comfort of travel. Then, the results of the analysis were compared with the results obtained using other multi-criteria decision-making support methods, i.e. ELECTRE I, AHP, TOPSIS, PROMETHEE, SAW, PVM. The considered methods were divided according to the way the result was presented, as a result of which the methods based on the relation of superiority (which included the MAJA method) and methods using ranking were distinguished, and then an intra-group comparison was made. On the basis of the constructed compliance matrix of the relation of superiority, it was found that domination methods exhibited convergence of the obtained results. However, in order to compare the convergence of the results of the ranking methods, the Spearman's linear correlation coefficient was used. The applied MAJA multi-criteria method has made it possible to determine non-dominated solutions considered optimal taking into account the adopted weights of criteria and compliance and non-compliance thresholds. Its unquestionable advantage is the possibility of using many partial criteria expressed in different measurement units. In the presented example, the best options were the premium express rail transport and airplane. The summary defines the direction of further research and possibilities of modification of the presented method.

We address the following decision problem. Given a numeration system U and a U-recognizable set X ⊆ ℕ , i.e. the set of its greedy U-representations is recognized by a finite automaton, decide whether or not X is ultimately periodic. We prove that this problem is decidable for a large class of numeration systems built on linear recurrence sequences. Based on arithmetical considerations about the recurrence equation and on p-adic methods, the DFA given as input provides a bound on the admissible periods to test. [ABSTRACT FROM AUTHOR]

DynaProg is an open-source MATLAB toolbox for solving multi-stage deterministic optimal decision problems using Dynamic Programming. This class of optimal control problems can be solved with Dynamic Programming (DP), which is a well-established optimal control technique suited for highly non-linear dynamic systems. Unfortunately, the numerical implementation of Dynamic Programming can be challenging and time consuming, which may discourage researchers from adopting it. The toolbox addresses these issues by providing a numerically fast DP optimization engine wrapped in a simple interface that allows the user to set up an optimal control problem in a straightforward yet flexible environment, with no restrictions on the controlled system’s simulation model. Therefore, it enables researchers to easily explore the usage of Dynamic Programming in their fields of expertise. Thorough documentation and a set of step-by-step examples complete the toolbox, thus allowing for easy deployment and providing insight of the optimization engine. Finally, the source code’s class-oriented design allows researchers experienced in Dynamic Programming to extend the toolbox if needed.

The article presents the possibility of using the PVM-VSI (Preference Vector Method - Vector Space of Increments) method in supporting the decision problem process, in which we choose one of several decision variants. However, these variants are assessed according to various criteria. Therefore, we need to have knowledge about the options under consideration. This knowledge is not always quantified. It is also important that the assessment of variants of the decision problem under consideration is independent of the preferences and opinions of the decision-maker, i.e. relatively objective. The article uses the PVM-VSI method [1] to support decisions related to the choice of an electric family car. The ranking is intended to indicate which car meets the usability requirements best defined by the decision maker, while meeting its visual preferences both in terms of appearance and interior. [ABSTRACT FROM AUTHOR]

Wastewater treatment (WWT) is a foremost challenge for maintaining the health of ecosystems and human beings; the waste products of the water-treatment process can be a problem or an opportunity. The sewage sludge (SS) produced during sewage treatment can be considered a waste to be disposed of in a landfill or as a source for obtaining raw material to be used as a fertilizer, building material, or alternative fuel source suitable for co-incineration in a high-temperature furnace. To this concern, this study's purpose consisted of developing a decision model, supported by an Artificial Neural Network (ANN model), allowing us to identify the most effective sludge management strategy in economic terms. Consistent with the aim of the work, the suitable SS treatment was identified, selecting for each phase of the SS treatment, an alternative available on the market ensuring energy and/or matter recovery, in line with the circular water value chain. Results show that the ANN model identifies the suitable SS treatments on multiple factors, thus supporting the decision-making and identifying the solution as per user requirements. [ABSTRACT FROM AUTHOR]

For communication systems there is a recent trend towards shifting functionalities from the physical layer to higher layers by enabling software-focused solutions. Having obtained a (physical layer-based) description of the communication channel, such approaches exploit this knowledge to enable various services by subsequently processing it on higher layers. For this it is a crucial task to first find out in which state the underlying communication channel is. This paper develops a framework based on Turing machines and studies whether or not it is in principle possible to algorithmically solve such classification tasks, i.e., to decide in which state the communication system is. Turing machines have no limitations on computational complexity, computing capacity and storage, and can simulate any given algorithm and therewith are a simple but very powerful model of computation. They characterize the fundamental performance limits for today’s digital computers. It is shown that there exists no Turing machine that takes the physical description of the communication channel as an input and solves a non-trivial classification task. Subsequently, this general result is used to study communication under adversarial attacks and it is shown that it is impossible to algorithmically detect denial-of-service (DoS) attacks on the transmission. Jamming attacks on ACK/NACK feedback cannot be detected as well and, in addition, ACK/NACK feedback is shown to be useless for the detection of DoS on the actual message transmission. Further applications are discussed including DoS attacks on the Post Shannon task of identification, and on physical layer security and resilience by design. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The present study proposes to analyse farmers' attitudes towards risk and examine the effect of specific socio-demographic and socio-economic characteristics on farmers' risk attitudes in irrigated and rain-fed regions of Odisha, India. A total of 400 randomly selected farmers participated in the experiment. The study applies the Modified Holt and Laury Lottery method for measuring risk attitudes. The majority of the farmers are having a risk-averse attitude and only a few farmers have a risk-taking attitude. One-sixth of the farmers are having risk-neutral decision behavior. The effect of Socio-demographic and socio-economic variables on farmers' risk attitude is also measured using an ordered probit model dealing with risky outcomes. The study reveals a negative relationship between household size and a risk-averse attitude. The study also reveals a negative relationship between off-farm income source and risk-averse attitude. The study also finds that there is an immediate need to improve extension facilities in the study area to train these farmers regarding the best risk management practices for deciding the choice of a particular crop such as growing short-duration crops as well as climate-resistant crop variety. Storage facilities need to be improved and there is an urgent need for improved irrigation systems to increase production particularly in Bolangir district. The result provides government agencies an outline to know how risky farming environment affects farmers' production decisions and designing policies such as crop insurance, weather-based crop insurance and other safety nets that effectively address farmer's problem. The main intention behind this experimental design is to make the policy makers aware of the high degree of risk aversion existing in a rural developing farm setting. Socio-demographic and socio-economic variables can be taken as a reference while implementing policies dealing with risky outcomes.

The paper presents the concept and functional requirements of an IT tool to assist in the development of adverse event scenarios and the location of this IT tool in the process of civil planning. In addition, the paper provides procedures: development of adverse events scenarios, determination of a decision problem and verification of safeguards proposed in response to identified threats to which the object under consideration is exposed.

In this article, I present a semantically natural conservative extension of Urquhart's positive semilattice logic with a sort of constructive negation. A subscripted sequent calculus is given for this logic and proofs of its soundness and completeness are sketched. It is shown that the logic lacks the finite model property. I discuss certain questions Urquhart has raised concerning the decision problem for the positive semilattice logic in the context of this logic and pose some problems for further research. [ABSTRACT FROM AUTHOR]

We define a new strict and computable hierarchy for the family of automaton semigroups, which reflects the various asymptotic behaviors of the state-activity growth. This hierarchy extends that given by Sidki for automaton groups, and also gives new insights into the latter. Its exponential part coincides with a notion of entropy for some associated automata. We prove that the Order Problem is decidable whenever the state-activity is bounded. The Order Problem remains open for the next level of this hierarchy, that is, when the state-activity is linear. Gillibert showed that it is undecidable in the whole family. We extend the aforementioned hierarchy via a semi-norm making it more coarse but somehow more robust and we prove that the Order Problem is still decidable for the first two levels of this alternative hierarchy. [ABSTRACT FROM AUTHOR]

Given an elementary cellular automaton and a cell v, we define the stability decision problem as the determination of whether or not the state of cell v will ever change, at least once, during the time evolution of the rule, over a finite input configuration. Here, we perform the study of the entire elementary cellular automata rule space, for the two possible decision cases of the problem, namely, changes in v from state 0 to 1 (0 → 1), and the other way round (1 → 0). Out of the 256 elementary cellular automata, we show that for all of them, at least one of the two decision problems is in the NC complexity class. [ABSTRACT FROM AUTHOR]

This paper represents a generic feature extraction approach to handle multiple attribute decision analysis problems. For that purpose, available decision support frameworks are carefully studied and the basic types of attributes involved in the decision problems are identified. Based on this analysis, a generic decision support scheme is proposed that can deal with all sorts of attributes in order to deduce the optimal solution for any decision problem. The proposed framework is capable of handling multiple attributes throughout the process of providing a flawless solution for the decision problem under both risk and uncertainty. This paper provides detailed information about the sources of uncertainty in the decision-making process and proposes a sophisticated approach for capturing all sorts of uncertainties. In the proposed approach, a cross assessment of every attribute against the corresponding attribute of the other alternatives is conducted to extract the significant features of an attribute. The relative importance of every attribute is considered as a supporting knowledge representation parameter in order to optimize the attribute-assessment process. The final decision is made based on the numerical scores seized by the alternatives. The paper also represents a numerical study to demonstrate the potential applications of the proposed methodology. [ABSTRACT FROM AUTHOR]

The paper considers a class of decision problems with an infinite time horizon that contains Markov decision problems as an important special case. Our interest concerns the case where the decision maker cannot commit himself to his future action choices. We model the decision maker as consisting of multiple selves, where each history of the decision problem corresponds to one self. Each self is assumed to have the same utility function as the decision maker. Our results are twofold: Firstly, we demonstrate that the set of subgame optimal policies coincides with the set of subgame perfect equilibria of the decision problem. Furthermore, the set of subgame optimal policies is contained in the set of optimal policies and the set of optimal policies is contained in the set of Nash equilibria. Secondly, we show that the set of pure subgame optimal policies is the unique minimal curb set of the decision problem. The concept of a subgame optimal policy is therefore robust to the absence of commitment technologies. [ABSTRACT FROM AUTHOR]