---
_id: '4511'
abstract:
- lang: eng
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.'
acknowledgement: This research was supported in part by the Swiss National Science
Foundation and by the NSF grant CCR-0225610.
alternative_title:
- LNCS
author:
- first_name: Thomas A
full_name: Thomas Henzinger
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
citation:
ama: 'Henzinger TA. Quantitative generalizations of languages. In: Vol 4588. Springer;
2007:20-22. doi:10.1007/978-3-540-73208-2_2'
apa: 'Henzinger, T. A. (2007). Quantitative generalizations of languages (Vol. 4588,
pp. 20–22). Presented at the DLT: Developments in Language Theory, Springer. https://doi.org/10.1007/978-3-540-73208-2_2'
chicago: Henzinger, Thomas A. “Quantitative Generalizations of Languages,” 4588:20–22.
Springer, 2007. https://doi.org/10.1007/978-3-540-73208-2_2.
ieee: 'T. A. Henzinger, “Quantitative generalizations of languages,” presented at
the DLT: Developments in Language Theory, 2007, vol. 4588, pp. 20–22.'
ista: 'Henzinger TA. 2007. Quantitative generalizations of languages. DLT: Developments
in Language Theory, LNCS, vol. 4588, 20–22.'
mla: Henzinger, Thomas A. *Quantitative Generalizations of Languages*. Vol.
4588, Springer, 2007, pp. 20–22, doi:10.1007/978-3-540-73208-2_2.
short: T.A. Henzinger, in:, Springer, 2007, pp. 20–22.
conference:
name: 'DLT: Developments in Language Theory'
date_created: 2018-12-11T12:09:14Z
date_published: 2007-06-21T00:00:00Z
date_updated: 2021-01-12T07:59:21Z
day: '21'
doi: 10.1007/978-3-540-73208-2_2
extern: 1
intvolume: ' 4588'
month: '06'
page: 20 - 22
publication_status: published
publisher: Springer
publist_id: '218'
quality_controlled: 0
status: public
title: Quantitative generalizations of languages
type: conference
volume: 4588
year: '2007'
...