@inproceedings{4594,
abstract = {The authors introduce two-way timed automata-timed automata that can move back and forth while reading a timed word. Two-wayness in its unrestricted form leads, like nondeterminism, to the undecidability of language inclusion. However, if they restrict the number of times an input symbol may be revisited, then two-wayness is both harmless and desirable. The authors show that the resulting class of bounded two-way deterministic timed automata is closed under all boolean operations, has decidable (PSPACE-complete) emptiness and inclusion problems, and subsumes all decidable real-time logics we know. They obtain a strict hierarchy of real-time properties: deterministic timed automata can accept more languages as the bound on the number of times an input symbol may be revisited is increased. This hierarchy is also enforced by the number of alternations between past and future operators in temporal logic. The combination of the results leads to a decision procedure for a real-time logic with past operators
},
author = {Alur, Rajeev and Thomas Henzinger},
pages = {177 -- 186},
publisher = {IEEE},
title = {{Back to the future: Towards a theory of timed regular languages}},
doi = {10.1109/SFCS.1992.267774},
year = {1992},
}
@inbook{3566,
author = {Herbert Edelsbrunner and Sharir, Micha},
booktitle = {Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift},
pages = {253 -- 263},
publisher = {American Mathematical Society},
title = {{A hyperplane incidence problem with applications to counting distances}},
volume = {4},
year = {1991},
}
@article{3648,
abstract = {We investigate the probability of fixation of a chromosome rearrangement in a subdivided population, concentrating on the limit where migration is so large relative to selection (m ≫ s) that the population can be thought of as being continuously distributed. We study two demes, and one- and two-dimensional populations. For two demes, the probability of fixation in the limit of high migration approximates that of a population with twice the size of a single deme: migration therefore greatly reduces the fixation probability. However, this behavior does not extend to a large array of demes. Then, the fixation probability depends primarily on neighborhood size (Nb), and may be appreciable even with strong selection and free gene flow (≈exp(-B·Nb) in one dimension, ≈exp(-B\cdotNb) in two dimensions). Our results are close to those for the more tractable case of a polygenic character under disruptive selection.},
author = {Nicholas Barton and Rouhani, Shahin},
journal = {Evolution},
number = {3},
pages = {499 -- 517},
publisher = {Wiley-Blackwell},
title = {{The probability of fixation of a new karyotype in a continuous population}},
volume = {45},
year = {1991},
}
@article{4052,
abstract = {This paper describes an effective procedure for stratifying a real semi-algebraic set into cells of constant description size. The attractive feature of our method is that the number of cells produced is singly exponential in the number of input variables. This compares favorably with the doubly exponential size of Collins' decomposition. Unlike Collins' construction, however, our scheme does not produce a cell complex but only a smooth stratification. Nevertheless, we are able to apply our results in interesting ways to problems of point location and geometric optimization.},
author = {Chazelle, Bernard and Herbert Edelsbrunner and Guibas, Leonidas J and Sharir, Micha},
journal = {Theoretical Computer Science},
number = {1},
pages = {77 -- 105},
publisher = {Elsevier},
title = {{A singly exponential stratification scheme for real semi-algebraic varieties and its applications}},
doi = {10.1016/0304-3975(91)90261-Y},
volume = {84},
year = {1991},
}
@article{4057,
author = {Herbert Edelsbrunner},
journal = {Journal of Computer and System Sciences},
number = {2},
pages = {249 -- 251},
publisher = {Elsevier},
title = {{Corrigendum}},
doi = {10.1016/0022-0000(91)90013-U},
volume = {42},
year = {1991},
}