Decision problems for patterns
Journal of Computer and System Sciences
A note on the equivalence problem of E-patterns
Information Processing Letters
Handbook of formal languages, vol. 1
Handbook of formal languages, vol. 1
On the equivalence problem for E-pattern languages
Theoretical Computer Science
Handbook of Formal Languages
Polynomial Time Inference of Extended Regular Pattern Languages
Proceedings of RIMS Symposium on Software Science and Engineering
The Relation of Two Patterns with Comparable Languages
STACS '88 Proceedings of the 5th Annual Symposium on Theoretical Aspects of Computer Science
On a conjecture about finite fixed points of morphisms
Theoretical Computer Science - Combinatorics on words
A non-learnable class of E-pattern languages
Theoretical Computer Science - Algorithmic learning theory(ALT 2002)
On the equivalence problem for e-pattern languages over small alphabets
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
Discontinuities in pattern inference
Theoretical Computer Science
Bad News on Decision Problems for Patterns
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Bad news on decision problems for patterns
Information and Computation
Theoretical Computer Science
| Hi-index | 0.00 |
Our paper contributes new facets to the discussion on the equivalence problem for E-pattern languages (also referred to as extended or erasing pattern languages). This fundamental open question asks for the existence of a computable function which, given any pair of patterns, decides whether or not they generate the same language. Our main result disproves Ohlebusch and Ukkonen's Conjecture (Theoretical Computer Science 186, 1997) on the equivalence problem; the respective argumentation - that largely deals with the nondeterminism of pattern languages and, thus, yields new insights into combinatories on morphisms in free monoids - is restricted to terminal alphabets with at most four distinct letters. Additionally and with regard to larger alphabets, we examine the standard proof technique which in previous works has successfully been applied to restricted variants of the equivalence problem, and we show that it has to be adapted in an unexpected manner if the full class of E-pattern languages is considered. This necessity of modifying the analysed method is caused by a strongly counter-intuitive phenomenon concerning the expressive power of injective morphisms.