Since the tech boom in the early 2000s, computer science, especially the study of algorithms and mathematics, has been prevalent to satisfy new needs for efficiency and convenience. The founding father of modern computer science, Alan Turing, proposes the foundation of modern computability theories known as the Turing Machine. This article is dedicated to exploring a variant of Turing's mathematical model, where the inputs become infinite and empirical. In a way, it is also an exploration of whether theoretically a true interactive machine can be achieved through a finite number of noninteractive machines. To prove it possible, this article utilizes methods such as researching from established papers, proof by deduction, and mathematical induction. In terms of articles, the main source is JSTOR. As the proof goes, it is mathematically proven in this essay that in terms of generic case K, an Interactive Machine A(K) shares the same explanatory equivalence with a finite number of Turing Machines T(K). It is said that A maps onto T.

Abstract. As a famous novel of the American literature, A Streetcar Named Desire represents Tennessee Williams" utmost achievement in fiction. Researchers are familiar with his undisguised description about symbolism in the novel, but less attention to the psychological realism in the novel. Psychological realism is the realistic writing that probes deeply into the complexities of characters" thoughts and motivations. Henry James is considered the founder of psychological realism. His novel The Ambassadors is considered to be a masterpiece of psychological realism. Tennessee Williams uses the psychological realism successfully in his play A Streetcar Named Desire. The thesis introduces the author of A Streetcar Named Desire, makes a research of his writing style by collecting and analyzing some of his works and expounds the background of this novel. The thesis used qualitative research techniques. The main purpose of this thesis is through the analysis of setting, characters, dialogue of work to show the psychological realism in A Streetcar Named Desire.

Only with independent personality can we have inner freedom, spiritual independence, our own judgment standard and rational judgment. Independent personality is a mature expression of a person. Independent personality is also an important manifestation of a country's civilization progress. Independent personality embodies the independence of personality and affects a person's thought and behavior. The lack of independent personality will lead to problems in college students' studies, life and emotion. Because the cultivation of independent personality of college students is very urgent, can be said to be urgent. In school education, social education, family education pay attention to the overall development of college students, in self-education pay attention to their own promotion, then it is possible to become a mature, stable, full of self-esteem, self-confidence, self-love and independent college students, can truly adult and become the pillars of society. Only with independent personality can we have inner freedom, spiritual independence, our own judgment standard and rational judgment. Independent personality is a mature expression of a person. Independent personality is also an important manifestation of a country's civilization progress. This paper discusses the reasons for the lack of independent personality of college students from four aspects: society, school, family and self, and puts forward some research countermeasures from these four aspects.