arXiv subjects
Publications and source records attributed to Farzad Didehvar.
Throughout this article we develop and change the definitions and the ideas in "arXiv:1006.4939", in order to consider the efficiency of functions and complexity time problems. The central idea here is effective enumeration and listing, and efficiency of function which is defined between two sets proposed in basic definitions. More in detail, it might be that h and g were co-order but the velocity of them be different.
In this paper we have investigated enumeration orders of elements of r.e. sets enumerated by means of Turing machines. We have defined a reducibility based on enumeration orders named "Enumeration Order Reducibility" on computable functions and also r.e. sets and studied their properties. Based on this reducibility we introduce an equivalence relation "Enumeration Order Equivalency". We have reached some properties of it. In subsequent, we have introduced another concept named "type-2 Enumeration Order Equivalency" and studied its properties too.
In this paper, we introduce a foundation for computable model theory of rational Pavelka logic (an extension of Łukasiewicz logic) and continuous logic, and prove effective versions of some theorems in model theory. We show how to reduce continuous logic to rational Pavelka logic. We also define notions of computability and decidability of a model for logics with computable, but uncountable, set of truth values; show that provability degree of a formula w.r.t. a linear theory is computable, and use this to carry out an effective Henkin construction. Therefore, for any effectively given consistent linear theory in continuous logic, we effectively produce its decidable model. This is the best possible, since we show that the computable model theory of continuous logic is an extension of computable model theory of classical logic. We conclude with noting that the unique separable model of a separably categorical and computably axiomatizable theory (such as that of a probability space or an $L^p$ Banach lattice) is decidable.
In this article we define a new reducibility based on the enumeration orders of r.e. sets.
An independent set in a graph G is a set of vertices no two of which are joined by an edge. A vertex-weighted graph associates a weight with every vertex in the graph. A vertex-weighted graph G is called a unique independence vertex-weighted graph if it has a unique independent set with maximum sum of weights. Although, in this paper we observe that the problem of recognizing unique independence vertex-weighted graphs is NP-hard in general and therefore no efficient characterization can be expected in general; we give, however, some combinatorial characterizations of unique independence vertex-weighted graphs. This paper introduces a motivating application of this problem in the area of combinatorial auctions, as well.
In this paper we offer a metric similar to graph edit distance which measures the distance between two (possibly infinite)weighted graphs with finite norm (we define the norm of a graph as the sum of absolute values of its edges). The main result is the completeness of the space. Some other analytical properties of this space are also investigated. The introduced metric could have some applications in pattern recognition and face recognition methods.
Could we define I? Throughout this article we give a negative answer to this question. More exactly, we show that there is no definition for I in a certain way. But this negative answer depends on our definition of definability. Here, we try to consider sufficient generalized definition of definability. In the middle of paper a paradox will arise which makes us to modify the way we use the concept of property and definability.
This paper investigates inventory management in a multi channel distribution system consisting of one manufacturer and an arbitrary number of retailers that face stochastic demand. Existence of the pure Nash equilibrium is proved and parameter restriction which implies uniqueness of it is derived. Also the Stackelberg game where the manufacturer plays a roll as a leader is discussed. Under specified parameter restrictions which guarantee profitability, sufficient condition for uniqueness of Stackelberg equilibrium is obtained. In addition comparison with simultaneous move game is made. The result shows that when whole prices are equal to production cost, manufacturer carries more inventory than simultaneous move game. Keywords: Inventory management, Substitution, Nash equilibrium, Stackelberg equilibrium.
In this paper, we have compared r.e. sets based on their enumeration orders with Turing machines. Accordingly, we have defined novel concept uniformity for Turing machines and r.e. sets and have studied some relationships between uniformity and both one-reducibility and Turing reducibility. Furthermore, we have defined type-2 uniformity concept and studied r.e. sets and Turing machines based on this concept. In the end, we have introduced a new structure called Turing Output Binary Search Tree that helps us lighten some ideas.