# Navigation in hypertext is easy only sometimes

Levene, Mark and Loizou, G.
(1999)
Navigation in hypertext is easy only sometimes.
*SIAM Journal on Computing* 29
(3),
pp. 728-760.
ISSN 0097-5397.

## Abstract

One of the main unsolved problems confronting Hypertext is the navigation problem, namely, the problem of having to know where you are in the database graph representing the structure of a Hypertext database, and knowing how to get to some other place you are searching for in the database graph. In order to tackle this problem we introduce a formal model for Hypertext. In this model a Hypertext database consists of an information repository, which stores the contents of the database in the form of pages, and a reachability relation, which is a directed graph describing the structure of the database. The notion of a trail, which is a path in the database graph describing some logical association amongst the pages in the trail, is central to our model. We define a Hypertext query language for our model based on a subset of propositional linear temporal logic, which we claim to be a natural formalism as a basis for establishing navigation semantics for Hypertext. The output of a trail query in this language is the set (which may be infinite) of all trails that satisfy the query. We show that there is a strong connection between the output of a trail query and finite automata in the sense that, given a Hypertext database and a trail query, we can construct a finite automaton representing the output of the query, which accepts a star-free regular language. We show that the construction of the finite automaton can be done in time exponential in the number of conjunctions, between the subformulas of the trail query, plus one. Given a Hypertext database and a trail query, the problem of deciding whether there exists a trail in the database that satisfies the trail query is referred to as the model checking problem. We show that, although this problem is NP-complete for different subsets of our query language, it can be solved in polynomial time for some significant special cases. Thus the navigation problem can only be efficiently solved in some special cases, and therefore in practice Hypertext systems could include algorithms which return randomized and/or fuzzy solutions.

## Metadata

Item Type: | Article |
---|---|

School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |

Depositing User: | Sarah Hall |

Date Deposited: | 07 Jun 2021 17:49 |

Last Modified: | 09 Aug 2023 12:51 |

URI: | https://eprints.bbk.ac.uk/id/eprint/44635 |

## Statistics

Additional statistics are available via IRStats2.