A Half-Century of Automata Theory最新文献

{"title":"Compositions over a Finite Domain: From Completeness to Synchronizable Automata","authors":"A. Salomaa","doi":"10.1142/9789812810168_0007","DOIUrl":"https://doi.org/10.1142/9789812810168_0007","url":null,"abstract":"We will consider functions whose domain is a fixed finite set N with n elements, n ≥ 2, and whose range is included in N. Such a setup occurs in many and very diverse situations. Depending on the interpretation, different questions will be asked. The two interpretations we have had mostly in mind are many-valued logic and finite deterministic automata. In the former, the set N consists of n truth values, and the functions are truth functions. In the latter, the set N consists of the states of an automaton, whereas each letter of the input alphabet induces a specific function: the next state when reading that letter. We will consider two specific issues concerning functions of the kind mentioned: completeness and complexity of compositions. While the former is fairly well understood, very little is known about the latter. Our starting point is an old conjecture, falling within the framework of the complexity of computations, concerning finite deterministic automata. Variants and generalizations of this conjecture are presented. It is also shown that the conjecture does not hold for functions of several variables","PeriodicalId":294477,"journal":{"name":"A Half-Century of Automata Theory","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124546674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Undecidability and Incompleteness Results in Automata Theory","authors":"J. Hartmanis","doi":"10.1142/9789812810168_0002","DOIUrl":"https://doi.org/10.1142/9789812810168_0002","url":null,"abstract":"Automata theory is inextricably intertwined with undecidability and incompleteness results. This papers explores the beautiful panorama of undecidability and Godel-like incompleteness results in automata theory that reveals their ubiquity and clarifies and illustrates how the severity of these results changes with the complexity of the problems and the computing power of the automata.","PeriodicalId":294477,"journal":{"name":"A Half-Century of Automata Theory","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122998512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Forty Years of Formal Power Series in Automata Theory","authors":"W. Kuich","doi":"10.1142/9789812810168_0004","DOIUrl":"https://doi.org/10.1142/9789812810168_0004","url":null,"abstract":"","PeriodicalId":294477,"journal":{"name":"A Half-Century of Automata Theory","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114730198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hazard Algebras (Extended Abstract)","authors":"J. Brzozowski, Z. Ésik","doi":"10.1142/9789812810168_0001","DOIUrl":"https://doi.org/10.1142/9789812810168_0001","url":null,"abstract":"We introduce algebras capable of representing, detecting, identifying, and counting static and dynamic hazard pulses on any wire in a gate circuit. These algebras also permit us to count the number of signal changes on any wire. This is of interest to logic designers for two reasons: each signal change consumes energy, and unnecessary multiple signal changes slow down the circuit operation. We describe efficient circuit simulation algorithms based on our algebras and illustrate them by several examples. Our method generalizes Eichelberger's ternary simulation and several other algebras designed for hazard detection.","PeriodicalId":294477,"journal":{"name":"A Half-Century of Automata Theory","volume":"04 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127225512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Playing Infinite Games in Finite Time","authors":"R. McNaughton","doi":"10.1142/9789812810168_0005","DOIUrl":"https://doi.org/10.1142/9789812810168_0005","url":null,"abstract":"Robert Wright dashes through ancient history to demonstrate how a certain type of information already present in nature—a type of mutual altruism known in game theory as a \" non-zero sum game \" — first shaped human societies and gave rise to civilization. This century, the cycles of non-zero games are accelerating, leading our economy to new heights and our culture to new horizons. But one of the many consequences of progress, Wright argues, is that certain forms of culture become inevitable—for instance, mass democracy, or the emerging Internet. The question of whether any technology is inevitable is one of the great unanswered social issues of our time; Wright has the most articulated answer on the politically incorrect side of those who argue that technology determines our fate. —KK Globalization, it seems to me, has been in the cards not just since the invention of the telegraph or the steamship, or even the written word or the wheel, but since the invention of life. • If you explore the murky recesses of just about any famously civilized people, you'll find this dark secret: they started out as barbarians. • Keep your eye on the memes. People and peoples come and go, live and die. But their memes, like their genes, persist. When all the trading and plundering and warring is done, bodies may be lying everywhere , and social structures may seem in disarray. Yet in the process, culture, the aggregate menu of memes on which society can draw, may well have evolved. • …Consider how hard people in nonliterate societies work to etch financial obligations in the public memory. The ostentatious Potlatch seems less absurd when viewed as a way to assemble a large audience to witness the incurring of a large debt. • For to deny any directionality in cultural evolution is to say that the aborigines, or the Shoshone, or the !Kung, left to their own devices, would show no natural tendency to propel their culture toward higher levels of technological sophistication and social complexity. • Today [a] vast interconnectedness, on a global scale, is obvious. But even in the Middle Ages, all of Eurasia and northern Africa had begun to constitute a single data-processing system. A slow system, yes, especially when trade would fall off after political dislocation—but a big system. The iron horseshoe and the windpipe friendly harness seem to have been invented in Asia …","PeriodicalId":294477,"journal":{"name":"A Half-Century of Automata Theory","volume":"147 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124355250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Automata Theory: Its Past and Future","authors":"J. Hopcroft","doi":"10.1142/9789812810168_0003","DOIUrl":"https://doi.org/10.1142/9789812810168_0003","url":null,"abstract":"This paper briefly reviews key advances in automata theory since 1960. It focuses on why certain lines of inquiry were followed, why others were not, and why some works were deemed more valuable to the discipline than others. I also compare the field today to what it was in 1960, with an eye toward areas in which the biggest breakthroughs are likely to occur in the future. Theoretical computer science may be poised for another period of significant advance, similar to that which occurred in the 1960's and 70's","PeriodicalId":294477,"journal":{"name":"A Half-Century of Automata Theory","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122700110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}