arXiv subjects

Rasoul Ramezanian

Publications and source records attributed to Rasoul Ramezanian.

16 recordsLinked to original sources

arXiv2026

Well-Defined but Not Predetermined Persistent Mathematical Objects, Embedded Observers, and the Provability of P = N P

We develop a foundational distinction between \emph{well-definedness} and \emph{predetermination}. A persistent mathematical or computational object may return a unique answer whenever a query is made and preserve every previously returned answer, while its answers to as-yet unqueried inputs are not represented by one completed, history-independent extension. We call such an object \emph{well-defined but non-predetermined}. We next formulate an observer-based semantics. All observers inhabit one shared computational world, their interactions modify one common global state, and they have access to one realized history. Under axioms of shared history, historical irreversibility, persistence, and historical indistinguishability, embedded observers cannot establish from the realized history alone whether its compatible extension was predetermined or progressively formed. A persistently evolutionary polynomial time computable oracle supplies a concrete example and yields a deterministic--nondeterministic separation under an explicitly history-sensitive semantics. We then derive a conditional result concerning the provability of $P=NP$. The conclusion is an observer-relative unprovability theorem, not an unconditional proof of classical $P\neq NP$.

math.LO↗

arXiv2026

Stable Matching with Payoff Guarantees

We consider a variant of the Assignment Game of Shapley and Shubik (1971), where agents do not observe the assignment or the surplus division of other matched pairs. We propose a set-valued solution concept (Self-Stabilizing Set) and characterize the largest such set. This leads to the formulation of the Stable Payoff Guarantee (SPG) set, which assumes that agents receive at least their payoff guarantees and that this is common knowledge. Our main result is that, for generic surplus matrices, the SPG set consists only of the efficient assignment. The associated payoff vectors are given by the smallest interval that contains the worker-optimal and firm-optimal stable payoffs.

econ.TH↗

arXiv2024

The Division Problem of Chances

In frequently repeated matching scenarios, individuals may require diversification in their choices. Therefore, when faced with a set of potential outcomes, each individual may have an ideal lottery over outcomes that represents their preferred option. This suggests that, as people seek variety, their favorite choice is not a particular outcome, but rather a lottery over them as their peak for their preferences. We explore matching problems in situations where agents' preferences are represented by ideal lotteries. Our focus lies in addressing the challenge of dividing chances in matching, where agents express their preferences over a set of objects through ideal lotteries that reflect their single-peaked preferences. We discuss properties such as strategy proofness, replacement monotonicity, (Pareto) efficiency, in-betweenness, non-bossiness, envy-freeness, and anonymity in the context of dividing chances, and propose a class of mechanisms called URC mechanisms that satisfy these properties. Subsequently, we prove that if a mechanism for dividing chances is strategy proof, (Pareto) efficient, replacement monotonic, in-between, non-bossy, and anonymous (or envy free), then it is equivalent in terms of welfare to a URC mechanism.

cs.GT↗

arXiv2023

The Temporal Continuum

The continuum has been one of the most controversial topics in mathematics since the time of the Greeks. Some mathematicians, such as Euclid and Cantor, held the position that a line is composed of points, while others, like Aristotle, Weyl and Brouwer, argued that a line is not composed of points but rather a matrix of a continued insertion of points. In spite of this disagreement on the structure of the continuum, they did distinguish the temporal line from the spatial line. In this paper, we argue that there is indeed a difference between the intuition of the spatial continuum and the intuition of the temporal continuum. The main primary aspect of the temporal continuum, in contrast with the spatial continuum, is the notion of orientation. The continuum has usually been mathematically modeled by Cauchy sequences and the Dedekind cuts. While in the first model, each point can be approximated by rational numbers, in the second one, that is not possible constructively. We argue that points on the temporal continuum cannot be approximated by rationals as a temporal point is a flow that sinks to the past. In our model, the continuum is a collection of constructive Dedekind cuts, and we define two topologies for temporal continuum: 1. oriented topology and 2. the ordinary topology. We prove that every total function from the oriented topological space to the ordinary one is continuous.

math.HO↗

arXiv2020

Preventing Social Disappointment in Elections

Mechanism design is concerned with settings where a policymaker (or social planner) faces the problem of aggregating the announced preferences of multiple agents into a collective (or social), system-wide decision. One of the most important ways for aggregating preference that has been used in multi-agent systems is election. In an election, the aim is to select the candidate who reflects the common will of society. Despite the importance of this subject, in some situations, the result of the election does not respect the purpose of those who execute it and the election leads to dissatisfaction of a large amount of people and in some cases causes polarization in societies. To analyze these situations, we introduce a new notion called social disappointment and we show which voting rules can prevent it in elections. In addition, we propose new protocols to prevent social disappointment in elections. A version of the impossibility theorem is proved regarding social disappointment in elections, showing that there is no voting rule for four or more candidates that simultaneously satisfies avoiding social disappointment and Condorcet winner criteria. We give conditions under which one of our new protocols always selects the Condorcet winner under the assumption of single peakedness. We empirically compare our protocols with seven well-known other voting protocols and observe that our protocols are capable of preventing social disappointment and are more robust against manipulations.

cs.MA↗

arXiv2020

A Formal Axiomatization of Computation

We introduce an axiomatization for the notion of computation. Based on the idea of Brouwer choice sequences, we construct a model, denoted by $E$, which satisfies our axioms and $E \models \mathrm{ P \neq NP}$. In other words, regarding "effective computability" in Brouwer intuitionism viewpoint, we show $\mathrm{ P \neq NP}$.

cs.CC↗

arXiv2019

Computer-Simulation Model Theory (P= NP is not provable)

The simulation hypothesis says that all the materials and events in the reality (including the universe, our body, our thinking, walking and etc) are computations, and the reality is a computer simulation program like a video game. All works we do (talking, reasoning, seeing and etc) are computations performed by the universe-computer which runs the simulation program. Inspired by the view of the simulation hypothesis (but independent of this hypothesis), we propose a new method of logical reasoning named "Computer-Simulation Model Theory", CSMT. Computer-Simulation Model Theory is an extension of Mathematical Model Theory where instead of mathematical-structures, computer-simulations are replaced, and the activity of reasoning and computing of the reasoner is also simulated in the model. (CSMT) argues that: For a formula $ϕ$, construct a computer simulation model $S$, such that 1- $ϕ$ does not hold in $S$, and 2- the reasoner $I$ $($human being, the one who lives inside the reality$)$ cannot distinguish $S$ from the reality $(R)$, then $I$ cannot prove $ϕ$ in reality. Although $\mathrm{CSMT}$ is inspired by the simulation hypothesis, but this reasoning method is independent of the acceptance of this hypothesis. As we argue in this part, one may do not accept the simulation hypothesis, but knows $\mathrm{CSMT}$ a valid reasoning method. As an application of Computer-Simulation Model Theory, we study the famous problem P vs NP. We let $ϕ\equiv\mathrm{ [P= NP]} $ and construct a computer simulation model $E$ such that $\mathrm{P= NP}$ does not hold in $E$.

cs.CC↗

arXiv2019

A process algebraic form to represent extensive games

In this paper, we introduce an agent-based representation of games, in order to propose a compact representation for multi-party games in game theory. Our method is inspired by concepts in process theory and process algebra. In addition, we introduce an algorithm whose input is a game in the form of process algebra (proposed in this paper) and as an output, finds the Nash equilibrium of the game in linear space complexity.

cs.GT↗

arXiv2015

A Hypercomputation in Brouwer's Constructivism

In contrast to other constructivist schools, for Brouwer, the notion of "constructive object" is not restricted to be presented as `words' in some finite alphabet of symbols, and choice sequences which are non-predetermined and unfinished objects are legitimate constructive objects. In this way, Brouwer's constructivism goes beyond Turing computability. Further, in 1999, the term hypercomputation was introduced by J. Copeland. Hypercomputation refers to models of computation which go beyond Church-Turing thesis. In this paper, we propose a hypercomputation called persistently evolutionary Turing machines based on Brouwer's notion of being constructive.

cs.LO↗

arXiv2014

A Computational Model and Convergence Theorem for Rumor Dissemination in Social Networks

The spread of rumors, which are known as unverified statements of uncertain origin, may cause tremendous number of social problems. If it would be possible to identify factors affecting spreading a rumor (such as agents' desires, trust network, etc.), then this could be used to slowdown or stop its spreading. A computational model that includes rumor features and the way a rumor is spread among society's members, based on their desires, is therefore needed. Our research is centering on the relation between the homogeneity of the society and rumor convergence in it and result shows that the homogeneity of the society is a necessary condition for convergence of the spreading rumor.

cs.SI↗

arXiv2014

Diffusion of Innovations over Multiplex Social Networks

The ways in which an innovation (e.g., new behaviour, idea, technology, product) diffuses among people can determine its success or failure. In this paper, we address the problem of diffusion of innovations over multiplex social networks where the neighbours of a person belong to one or multiple networks (or layers) such as friends, families, or colleagues. To this end, we generalise one of the basic game-theoretic diffusion models, called networked coordination game, for multiplex networks. We present analytical results for this extended model and validate them through a simulation study, finding among other properties a lower bound for the success of an innovation.While simple and leading to intuitively understandable results, to the best of our knowledge this is the first extension of a game-theoretic innovation diffusion model for multiplex networks and as such it provides a basic framework to study more sophisticated innovation dynamics.

cs.SI↗

arXiv2014

Non-predetermined Model Theory

This article introduce a new model theory call non-predetermined model theory where functions and relations need not to be determined already and they are determined through time.

math.LO↗

arXiv2013

Disappointment in Social Choice Protocols

Social choice theory is a theoretical framework for analysis of combining individual preferences, interests, or welfare to reach a collective decision or social welfare in some sense. We introduce a new criterion for social choice protocols called social disappointment. Social disappointment happens when the outcome of a voting system occurs for those alternatives which are at the end of at least half of individual preference profiles. Here we introduce some protocols that prevent social disappointment and prove an impossibility theorem based on this key concept.

cs.MA↗

arXiv2013

A Constructive Epistemic Logic with Public Announcement (Non-Predetermined Possibilities)

We argue that the notion of epistemic \emph{possible worlds} in constructivism (intuitionism) is not as the same as it is in classic view, and there are possibilities, called non-predetermined worlds, which are ignored in (classic) Epistemic Logic. Regarding non-predetermined possibilities, we propose a constructive epistemic logic and prove soundness and completeness theorems for it. We extend the proposed logic by adding a public announcement operator. To declare the significance of our work, we formulate the well-known Surprise Exam Paradox, $\mathbf{SEP}$, via the proposed constructive epistemic logic and then put forward a solution for the paradox. We clarify that the puzzle in the $\mathbf{SEP}$ is because of students'(wrong) assumption that the day of the exam is necessarily predetermined.

cs.LO↗

arXiv2012

Computation Environments (2) Persistently Evolutionary Semantics

In the manuscript titled "Computation environment (1)", we introduced a notion called computation environment as an interactive model for computation and complexity theory. In this model, Turing machines are not autonomous entities and find their meanings through the interaction between a computist and a universal processor, and thus due to evolution of the universal processor, the meanings of Turing machines could change. In this manuscript, we discuss persistently evolutionary intensions. We introduce a new semantics, called persistently evolutionary semantics, for predicate logic that the meaning of function and predicate symbols are not already predetermined, and predicate and function symbols find their meaning through the interaction of the subject with the language. In (classic) model theory, the mathematician who studies a structure is assumed as a god who lives out of the structure, and the study of the mathematician does not effect the structure. The meaning of predicate and function symbols are assumed to be independent of the mathematician who does math. The persistently evolutionary semantics could be regarded as a start of "Interactive Model Theory" as a new paradigm in model theory (similar to the paradigm of interactive computation). In interactive model theory, we suppose that a mathematical structure should consist of two parts: 1) an intelligent agent (a subject), and 2) an environment (language), and every things should find its meaning through the interaction of these two parts. We introduce persistently evolutionary Kripke structure for propositional and predicate logic. Also, we propose a persistently evolutionary Kripke semantics for the notion of computation, where the intension of a code of a Turing machine persistently evolve. We show that in this Kripke model the subject can never know P = NP.

cs.LO↗

arXiv2012

Computation Environments, An Interactive Semantics for Turing Machines (which P is not equal to NP considering it)

To scrutinize notions of computation and time complexity, we introduce and formally define an interactive model for computation that we call it the \emph{computation environment}. A computation environment consists of two main parts: i) a universal processor and ii) a computist who uses the computability power of the universal processor to perform effective procedures. The notion of computation finds it meaning, for the computist, through his \underline{interaction} with the universal processor. We are interested in those computation environments which can be considered as alternative for the real computation environment that the human being is its computist. These computation environments must have two properties: 1- being physically plausible, and 2- being enough powerful. Based on Copeland' criteria for effective procedures, we define what a \emph{physically plausible} computation environment is. We construct two \emph{physically plausible} and \emph{enough powerful} computation environments: 1- the Turing computation environment, denoted by $E_T$, and 2- a persistently evolutionary computation environment, denoted by $E_e$, which persistently evolve in the course of executing the computations. We prove that the equality of complexity classes $\mathrm{P}$ and $\mathrm{NP}$ in the computation environment $E_e$ conflicts with the \underline{free will} of the computist. We provide an axiomatic system $\mathcal{T}$ for Turing computability and prove that ignoring just one of the axiom of $\mathcal{T}$, it would not be possible to derive $\mathrm{P=NP}$ from the rest of axioms. We prove that the computist who lives inside the environment $E_T$, can never be confident that whether he lives in a static environment or a persistently evolutionary one.

cs.CC↗