REPRESENTATION OF SEMIAUTOMATA BY CANONICAL WORDS AND EQUIVALENCES

2005 ◽  
Vol 16 (05) ◽  
pp. 831-850 ◽  
Author(s):  
JANUSZ BRZOZOWSKI ◽  
HELMUT JÜRGENSEN
Keyword(s):  
Simple Algorithm ◽  
The State ◽  
Closed Sets ◽  
Spanning Forest ◽  
Rewriting System ◽  
Special Cases ◽  
Software Modules ◽  
Canonical Representative ◽  
Rewriting Rules

We study a novel representation of semiautomata, which is motivated by the method of trace-assertion specifications of software modules. Each state of the semiautomaton is represented by an arbitrary word leading to that state, the canonical word. The transitions of the semiautomaton give rise to a right congruence, the state-equivalence, on the set of input words of the semiautomaton: two words are state-equivalent if and only if they lead to the same state. We present a simple algorithm for finding a set of generators for state-equivalence. Directly from this set of generators, we construct a confluent prefix-rewriting system which permits us to transform any word to its canonical representative. In general, the rewriting system may allow infinite derivations. To address this issue, we impose the condition of prefix-continuity on the set of canonical words. A set is prefix-continuous if, whenever a word w and a prefix u of w are in the set, then all the prefixes of w longer than u are also in the set. Prefix-continuous sets include prefix-free and prefix-closed sets as special cases. We prove that the rewriting system is Noetherian if and only if the set of canonical words is prefix-continuous. Furthermore, if the set of canonical words is prefix-continuous, then the set of rewriting rules is irredundant. We show that each prefix-continuous canonical set corresponds to a spanning forest of the semiautomaton.

Optimal replacement under a general failure model

1978 ◽  
Vol 10 (2) ◽  
pp. 431-451 ◽  
Author(s):  
Bo Bergman
Keyword(s):  
Threshold Value ◽  
Rate Function ◽  
The State ◽  
Failure Rate Function ◽  
State Variable ◽  
Optimal Replacement ◽  
State Dependent ◽  
Long Run ◽  
Special Cases ◽  
Dependent Failure

Replacement policies based on measurements of some increasing state variable, e.g. wear, accumulated damage or accumulated stress, are studied in this paper. It is assumed that the state measurements may be regarded as realizations of some stochastic process and that the proneness to failure of an active unit may be described by an increasing state-dependent failure rate function. Average long-run cost per unit time is considered. The optimal replacement rule is shown to be a control limit rule, i.e. it is optimal to replace either at failure or when the state variable has reached some threshold value, whichever occurs first. The optimal rule is determined. Some generalizations and special cases are given.

Coherence of subsumption, minimum typing and type-checking in F ≤

1992 ◽  
Vol 2 (1) ◽  
pp. 55-91 ◽  
Author(s):  
Pierre-Louis Curien ◽  
Giorgio Ghelli
Keyword(s):  
Normal Form ◽  
Type System ◽  
Lambda Calculus ◽  
Complete Information ◽  
Second Order ◽  
Semantic Interpretation ◽  
Type Checking ◽  
Rewriting System ◽  
Different Types ◽  
Rewriting Rules

A subtyping relation ≤ between types is often accompanied by a typing rule, called subsumption: if a term a has type T and T≤U, then a has type U. In presence of subsumption, a well-typed term does not codify its proof of well typing. Since a semantic interpretation is most naturally defined by induction on the structure of typing proofs, a problem of coherence arises: different typing proofs of the same term must have related meanings. We propose a proof-theoretical, rewriting approach to this problem. We focus on F≤, a second-order lambda calculus with bounded quantification, which is rich enough to make the problem interesting. We define a normalizing rewriting system on proofs, which transforms different proofs of the same typing judgement into a unique normal proof, with the further property that all the normal proofs assigning different types to a given term in a given environment differ only by a final application of the subsumption rule. This rewriting system is not defined on the proofs themselves but on the terms of an auxiliary type system, in which the terms carry complete information about their typing proof. This technique gives us three different results:— Any semantic interpretation is coherent if and only if our rewriting rules are satisfied as equations.— We obtain a proof of the existence of a minimum type for each term in a given environment.— From an analysis of the shape of normal form proofs, we obtain a deterministic typechecking algorithm, which is sound and complete by construction.

Filters and parameter estimation for a partially observable system subject to random failure with continuous-range observations

2004 ◽  
Vol 36 (4) ◽  
pp. 1212-1230 ◽  
Author(s):  
Daming Lin ◽  
Viliam Makis
Keyword(s):  
Condition Monitoring ◽  
Continuous Time ◽  
The State ◽  
Parameter Estimates ◽  
State Process ◽  
Observation Process ◽  
Special Cases ◽  
Random Failure ◽  
Prediction Problems ◽  
Continuous Range

We consider a failure-prone system operating in continuous time. Condition monitoring is conducted at discrete time epochs. The state of the system is assumed to evolve as a continuous-time Markov process with a finite state space. The observation process with continuous-range values is stochastically related to the state process, which, except for the failure state, is unobservable. Combining the failure information and the condition monitoring information, we derive a general recursive filter, and, as special cases, we obtain recursive formulae for the state estimation and other quantities of interest. Updated parameter estimates are obtained using the expectation-maximization (EM) algorithm. Some practical prediction problems are discussed and finally an illustrative example is given using a real dataset.

scholarly journals Z PROBLEMATYKI PRZEKSZTAŁCENIA PRAWA UŻYTKOWANIA WIECZYSTEGO W PRAWO WŁASNOŚCI

2017 ◽  
Vol 3 (2) ◽  
pp. 63
Author(s):  
Adam Brzozowski
Keyword(s):  
Local Governments ◽  
Current System ◽  
Common Knowledge ◽  
Rational Solution ◽  
Status Quo ◽  
The State ◽  
Property Right ◽  
Special Cases ◽  
The Status ◽  
The Right

From the Problems of a Transformation from Perpetual Usufruct to Property RightSummaryAn analysis of a normative state and a practice of a conduct of legal transactions with reference to legal regulations of perpetual usufruct and also of a transformation of this right into property right permits a statement that in Polish Law there came into being a system of norms completely unintelligible, excessively complicated, internally contradictory, bureaucratic and too costly for the national budget, local governments and perpetual usufructuaries. The primary cause of the status quo was the lack of a clearly defined objective at which the legislator was aiming. Expediency was implemented at the expense of system principles. It led to interventions of the Constitutional Tribunal. The legislator hedged, made successive provisions not only internally contradictory but also arousing new doubts as to their compliance with the Constitution of the Republic of Poland.It seems that the only rational solution of the status quo is to forego the right of perpetual usufruct by enfranchising perpetual usufructuaries. However, it has to be a regulation based on foundations completely different than these hitherto existing.The transformation should cover all perpetual usufructuaries, regardless of the mode and the time of their acquisition of this right, and should ensue ex lege. This would result in a significant simplification of a construction of the transformation. Given a tremendous interest of perpetual usufructuaries in the transformation, it would significantly reduce the amount of office labour and attendant costs incurred by them. At the same time affranchisement would become universal. Further simplification and lowering costs of transformation would require that entries in mortgage registers should be evidenced ex officio at the time of the first transaction relating to a given mortgage register. Since affranchisement in a discussed mode would cover all perpetual usufructuaries ex lege, it would be obvious that persons evidenced in a register as perpetual usufructuaries are property owners until a new entry is made.There should be no exception from the basic principle of universality of affranchisement of perpetual usufructuaries. It has to be assumed that land charged with perpetual usufruct has not been indispensable for the hitherto existing owner (the State Treasury, local government units) in order to perform their basic tasks. In special cases these units may employ an expropriation.The most difficult problem of the hitherto existing regulations faced has been the question of compensation due to hitherto owners from the fact of a loss of ownership as a result of a transformation. I propose to regulate these settlements in such a way that an enfranchised perpetual usufructuary should be charged with such performances as he was charged with hitherto as a perpetual usufructuary. In other words: he would be charged with an obligation to pay annuity during a period for which he has been granted, the right to perpetual usufruct, transformed into property right. In exchange for a performance, which in any case he would have to provide as per agreement, the former perpetual usufructuary would obtain a better right - property right. According to the proposition under discussion, the regulation would have a system character, in a long-term it would allow to effect such a reform of public finances that hitherto existing owners could perform their assigned tasks financing them from performances of a tribute type, and not from perpetual usufruct. One would have to consider the advisability of maintaining in force the principles of determining an amount of an annuity. It seems that instead of the current system (expensive and inefficient) there should be introduced a principle of a yearly raising of annuity according to a rate of inflation.It’s common knowledge that appreciable part of immovables of the State Treasury and municipal immovables originate from different kinds of „expropriations” carried out in the period of PRL [People’s Republic of Poland]. To secure claims of former owners I propose to create a special fund, meant for indemnities satisfying these claims, from obligatory written off amounts gained from receipts from former perpetual usufructuaries.

scholarly journals The Politicization of Society and the Religious Issues in Modern Russia

2020 ◽  
Vol 22 (4) ◽  
pp. 647-663
Author(s):  
Vasily K. Pinkevich
Keyword(s):  
The State ◽  
Private Life ◽  
Russian Society ◽  
Ruling Class ◽  
Extensive Discussion ◽  
Religious Policy ◽  
Special Cases ◽  
The One ◽  
The Right ◽  
High Level

The purpose of the article is to trace the connection between the change in the religious policy of the state and the anti-clerical protests of the 2016-2020s. Statements against Church restitution and the construction of churches have caused extensive discussion, which has given rise to a number of contradictory, sometimes mutually exclusive interpretations. According to the author, the reason for these protests was not private reasons, but deeper reasons related to the religious policy of the state. The author pays special attention to changes in religious legislation, which led to increased control over the private life of citizens and infringement of the right to freedom of ideological choice. The article points out that the religious issue has divided Russian society: the ruling class on the one hand, and a significant part of citizens on the other, have become increasingly different in understanding the place and role of religion in the life of the country. According to the author, the protests in Yekaterinburg, St. Petersburg, and Moscow were special cases of numerous manifestations of politicization of society and growing dissatisfaction with the state of state-confessional relations in modern Russia. The author concludes that the degree of conflict, the high level of solidarity actions, a diverse and resonant series of events, as well as the level of ideological discussion allow us to classify these events as political and plebiscite.

General optimal stopping theorems for semi-Markov processes

1993 ◽  
Vol 25 (4) ◽  
pp. 825-846 ◽  
Author(s):  
Frans A. Boshuizen ◽  
José M. Gouweleeuw
Keyword(s):  
Markov Processes ◽  
Optimal Stopping ◽  
Stopping Time ◽  
General Setting ◽  
The State ◽  
Shock Models ◽  
Special Cases ◽  
Optimal Stopping Problems ◽  
The Times ◽  
Semi Markov Processes

In this paper, optimal stopping problems for semi-Markov processes are studied in a fairly general setting. In such a process transitions are made from state to state in accordance with a Markov chain, but the amount of time spent in each state is random. The times spent in each state follow a general renewal process. They may depend on the present state as well as on the state into which the next transition is made.Our goal is to maximize the expected net return, which is given as a function of the state at time t minus some cost function. Discounting may or may not be considered. The main theorems (Theorems 3.5 and 3.11) are expressions for the optimal stopping time in the undiscounted and discounted case. These theorems generalize results of Zuckerman [16] and Boshuizen and Gouweleeuw [3]. Applications are given in various special cases.The results developed in this paper can also be applied to semi-Markov shock models, as considered in Taylor [13], Feldman [6] and Zuckerman [15].

IMPROVED NET REWRITING SYSTEMS–EXTENDED PETRI NETS SUPPORTING DYNAMIC CHANGES

2008 ◽  
Vol 17 (06) ◽  
pp. 1027-1052 ◽  
Author(s):  
JUN LI ◽  
XIANZHONG DAI ◽  
ZHENGDA MENG ◽  
LIBO XU
Keyword(s):  
Petri Nets ◽  
The State ◽  
Automated Manufacturing ◽  
Dynamic Changes ◽  
Manufacturing Cell ◽  
Rewriting Systems ◽  
Rewriting System ◽  
Practical System ◽  
Extended Petri Nets

The existing extensions of Petri nets supporting dynamic changes cannot ensure preservation of desired properties of the modeled systems. This paper tries to address this problem. By extending the structure of the net rewriting system (NRS) and modifying the specification of its rewriting rule, we present improved net rewriting system (INRS). INRS enjoys four important properties, i.e., locality, transitivity, reflexivity, and reversibility. A practical system subject to dynamic changes can be modeled by an INRS, and its desired properties can be preserved with the state evolvement of the INRS. The property-preserving principles of INRS and their strict proofs are provided as well. Finally, a case study is provided to demonstrate the modeling of an automated manufacturing cell with changeable structure using an INRS. The result shows that the desired properties of the cell are still preserved despite its model evolvement.

scholarly journals Intermediate rings of complex-valued continuous functions

2021 ◽  
Vol 22 (1) ◽  
pp. 47
Author(s):  
Amrita Acharyya ◽  
Sudip Kumar Acharyya ◽  
Sagarmoy Bag ◽  
Joshua Sack
Keyword(s):  
Algebraic Closure ◽  
Continuous Functions ◽  
Prime Ideals ◽  
Closed Field ◽  
Completely Regular ◽  
Closed Sets ◽  
Maximal Ideals ◽  
Special Cases ◽  
Necessary And Sufficient ◽  
Complex Valued

<p>For a completely regular Hausdorff topological space X, let C(X, C) be the ring of complex-valued continuous functions on X, let C ∗ (X, C) be its subring of bounded functions, and let Σ(X, C) denote the collection of all the rings that lie between C ∗ (X, C) and C(X, C). We show that there is a natural correlation between the absolutely convex ideals/ prime ideals/maximal ideals/z-ideals/z ◦ -ideals in the rings P(X, C) in Σ(X, C) and in their real-valued counterparts P(X, C) ∩ C(X). These correlations culminate to the fact that the structure space of any such P(X, C) is βX. For any ideal I in C(X, C), we observe that C ∗ (X, C)+I is a member of Σ(X, C), which is further isomorphic to a ring of the type C(Y, C). Incidentally these are the only C-type intermediate rings in Σ(X, C) if and only if X is pseudocompact. We show that for any maximal ideal M in C(X, C), C(X, C)/M is an algebraically closed field, which is furthermore the algebraic closure of C(X)/M ∩C(X). We give a necessary and sufficient condition for the ideal CP (X, C) of C(X, C), which consists of all those functions whose support lie on an ideal P of closed sets in X, to be a prime ideal, and we examine a few special cases thereafter. At the end of the article, we find estimates for a few standard parameters concerning the zero-divisor graphs of a P(X, C) in Σ(X, C).</p>

Recursive filters for a partially observable system subject to random failure

2003 ◽  
Vol 35 (1) ◽  
pp. 207-227 ◽  
Author(s):  
Daming Lin ◽  
Viliam Makis
Keyword(s):  
Condition Monitoring ◽  
Continuous Time ◽  
The State ◽  
Parameter Estimates ◽  
State Process ◽  
Observation Process ◽  
Special Cases ◽  
Random Failure ◽  
Partially Observable System ◽  
Prediction Problems

We consider a failure-prone system which operates in continuous time and is subject to condition monitoring at discrete time epochs. It is assumed that the state of the system evolves as a continuous-time Markov process with a finite state space. The observation process is stochastically related to the state process which is unobservable, except for the failure state. Combining the failure information and the information obtained from condition monitoring, and using the change of measure approach, we derive a general recursive filter, and, as special cases, we obtain recursive formulae for the state estimation and other quantities of interest. Up-dated parameter estimates are obtained using the EM algorithm. Some practical prediction problems are discussed and an illustrative example is given using a real dataset.

The geometry of closed sets in the state of chemical transformation

2015 ◽  
Vol 119 (3) ◽  
pp. 1633-1651 ◽  
Author(s):  
V. V. Klyucharev ◽  
S. V. Klyuchareva
Keyword(s):  
Chemical Transformation ◽  
The State ◽  
Closed Sets
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