{"product_id":"finite-automata-formal-logic-and-circuit-complexity-progress-in-theoretical-computer-science-9780817637194","title":"Finite Automata  Formal Logic  and Circuit Complexity (Progress in Theoretical Computer Science)","description":"\u003cp\u003eThe study of the connections between mathematical automata and for mal logic is as old as theoretical computer science itself. In the founding paper of the subject  published in 1936  Turing showed how to describe the behavior of a universal computing machine with a formula of first order predicate logic  and thereby concluded that there is no algorithm for deciding the validity of sentences in this logic. Research on the log ical aspects of the theory of finite-state automata  which is the subject of this book  began in the early 1960s with the work of J. Richard Biichi on monadic second-order logic. Biichis investigations were extended in several directions. One of these  explored by McNaughton and Papert in their 1971 monograph Counter-free Automata  was the characterization of automata that admit first-order behavioral descriptions  in terms of the semigroup theoretic approach to automata that had recently been developed in the work of Krohn and Rhodes and of Schiitzenberger. In the more than twenty years that have passed since the appearance of McNaughton and Paperts book  the underlying semigroup theory has grown enor mously  permitting a considerable extension of their results. During the same period  however  fundamental investigations in the theory of finite automata by and large fell out of fashion in the theoretical com puter science community  which moved to other concerns.\u003c\/p\u003e","brand":"My Store","offers":[{"title":"Default Title","offer_id":45665990606901,"sku":"ByrdShop_0817637192","price":186.1,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0627\/8139\/0901\/files\/9780817637194.jpg?v=1782414951","url":"https:\/\/atxbooks.com\/products\/finite-automata-formal-logic-and-circuit-complexity-progress-in-theoretical-computer-science-9780817637194","provider":"ATX Books","version":"1.0","type":"link"}