{"_id":"4511","abstract":[{"text":"In the traditional view, a language is a set of words, i.e., a function from words to boolean values. We call this view “qualitative,” because each word either belongs to or does not belong to a language. Let Σ be an alphabet, and let us consider infinite words over Σ. Formally, a qualitative language over Σ is a function A: B . There are many applications of qualitative languages. For example, qualitative languages are used to specify the legal behaviors of systems, and zero-sum objectives of games played on graphs. In the former case, each behavior of a system is either legal or illegal; in the latter case, each outcome of a game is either winning or losing. For defining languages, it is convenient to use finite acceptors (or generators). In particular, qualitative languages are often defined using finite-state machines (so-called ω-automata) whose transitions are labeled by letters from Σ. For example, the states of an ω-automaton may represent states of a system, and the transition labels may represent atomic observables of a behavior. There is a rich and well-studied theory of finite-state acceptors of qualitative languages, namely, the theory of theω-regular languages.","lang":"eng"}],"extern":1,"conference":{"name":"DLT: Developments in Language Theory"},"date_published":"2007-06-21T00:00:00Z","publication_status":"published","citation":{"ieee":"T. A. Henzinger, “Quantitative generalizations of languages,” presented at the DLT: Developments in Language Theory, 2007, vol. 4588, pp. 20–22.","mla":"Henzinger, Thomas A. <i>Quantitative Generalizations of Languages</i>. Vol. 4588, Springer, 2007, pp. 20–22, doi:<a href=\"https://doi.org/10.1007/978-3-540-73208-2_2\">10.1007/978-3-540-73208-2_2</a>.","short":"T.A. Henzinger, in:, Springer, 2007, pp. 20–22.","ista":"Henzinger TA. 2007. Quantitative generalizations of languages. DLT: Developments in Language Theory, LNCS, vol. 4588, 20–22.","chicago":"Henzinger, Thomas A. “Quantitative Generalizations of Languages,” 4588:20–22. Springer, 2007. <a href=\"https://doi.org/10.1007/978-3-540-73208-2_2\">https://doi.org/10.1007/978-3-540-73208-2_2</a>.","apa":"Henzinger, T. A. (2007). Quantitative generalizations of languages (Vol. 4588, pp. 20–22). Presented at the DLT: Developments in Language Theory, Springer. <a href=\"https://doi.org/10.1007/978-3-540-73208-2_2\">https://doi.org/10.1007/978-3-540-73208-2_2</a>","ama":"Henzinger TA. Quantitative generalizations of languages. In: Vol 4588. Springer; 2007:20-22. doi:<a href=\"https://doi.org/10.1007/978-3-540-73208-2_2\">10.1007/978-3-540-73208-2_2</a>"},"month":"06","date_updated":"2021-01-12T07:59:21Z","type":"conference","day":"21","author":[{"first_name":"Thomas A","last_name":"Henzinger","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","full_name":"Thomas Henzinger","orcid":"0000−0002−2985−7724"}],"doi":"10.1007/978-3-540-73208-2_2","page":"20 - 22","alternative_title":["LNCS"],"title":"Quantitative generalizations of languages","quality_controlled":0,"acknowledgement":"This research was supported in part by the Swiss National Science Foundation and by the NSF grant CCR-0225610.","status":"public","year":"2007","publisher":"Springer","intvolume":"      4588","publist_id":"218","volume":4588,"date_created":"2018-12-11T12:09:14Z"}