On Some Questions of Rationality and Decidability
نویسنده
چکیده
In this note we begin by resolving (in the negative) a question posed by Paz [6, Open Problem 1, p. 65] concerning the existence of an effective procedure for determining whether a recursively specified "probabilistie input-output relation" is of finite rank. To show that such an algorithm does not exist, it is enough to prove the undecidability of the corresponding problem for "probabilistic word functions" (take an input alphabet of one letter). The undecidability of rationality for general word functions is used in the proof of the above. This was proved by Paz [7, Corollary E3]. This problem, however, can be posed in much more generality: One might ask about the rationality of power series with coefficients in more general semirings. We give in Part 2 a completely new proof of the undeeidability result of Paz. This proof extends readily to the more general situation. For this we note that over a large class of semirings R (namely, those embeddable in commutative rings), unambiguous R-rational power series are recognizable languages. Particular cases of this latter result were already known. For example, the one-letter ease with coefficients in a field of characteristic zero follows from results on supports as in [2, Proposition I. 4.1.1]. The case of arbitrary alphabets and positive semirings is treated in [1, Corollary VIII. 4.3]. For the real numbers the result depends on the theory of isolated cutpoints as in [6, Theorem III. 13. 2.3]. The proof of the recognizability of R-rational series rests upon some new facts
منابع مشابه
تردید در وجود تلقی جهانشمول از عقلانیت در رویههای شهرسازی
There is a deep-seated belief among planners that the historical association between urban planning and rationality is an unquestioned presumption which they follow their daily practices based on. It seems that truth of urban planning claims has been shown predominantly by applying the concept of rationality. As a result, reflection on rationality can be taken into consideration as an importan...
متن کاملRationality in the Epistemic Geometry of Hujurat Surah Commentary
The conflict between rationality and devotion is rooted from an inappropriate comprehension about status of reason in epistemic system of religion and also being unfamiliar with pure and vital educations. Although some of the educations from the Divine Book have devotional prospects and are out of the reach of conventional reason, pondering in verses indicates that this does not mean digressing...
متن کاملDynamic system of strategic games
Maybe an event can't be modeled completely through one game but there is more chance with several games. With emphasis on players' rationality, we present new properties of strategic games, which result in production of other games. Here, a new attitude to modeling will be presented in game theory as dynamic system of strategic games and its some applications such as analysis of the clash betwe...
متن کاملThe Pathology of People's Viewpoints in implementation Of Urban Development Plans - Case Study of Sari City
Urban development plans are provided with a surface attitude to the economic, social, and physical dimensions of cities in Iran.. The purpose of this paper is to investigate the ecology of urban development projects in Iran. This is a case study of urban constructs with a social approach and phenomenology. The research questions are follows as: 1. What are the implications of the existing ratio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comput. Syst. Sci.
دوره 11 شماره
صفحات -
تاریخ انتشار 1975