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| Content Provider | ACM Digital Library |
|---|---|
| Author | Nivat, Maurice |
| Abstract | We recall that the Dyck language on the alphabet of 2n letters X &equil; {x1,.,xn,&xmarc;1,.,&xmarc;n} is the equivalence class of the empty word 1 ε X@@@@ modulo the Thue congruence generated on X@@@@ by the 2n relations xi&xmarc;i &equil; &xmarc;ixi &equil; 1 i ε {1,.,n}. Indeed for all n ε X@@@@ the equivalence class of n modulo this congruence is a non ambiguous algebraic (ie. context-free) language, the complement of which is also a non ambiguous algebraic language. The same situation is true for the congruence generated on X@@@@ by the n relations xi&xmarc;i &equil; 1 i ε {1,.,n}. The author convinced himself that many other congruences have the same property [Ni 1], and undertook the task of finding them systematically. Here is presented a part of the results of this undertaking. An important family of congruences is brought to light which have interesting decidability properties: in the constructions leading to these decidability properties we used as a guide line the nice paper of Mac Naughton [McN]. Sufficient conditions are given in order that the equivalence classes (and their complements) of such a congruence be an algebraic language. We do not study in this paper the properties of these languages, this will be done elsewhere [Ni 2]. |
| Starting Page | 221 |
| Ending Page | 225 |
| Page Count | 5 |
| File Format | |
| DOI | 10.1145/800161.805168 |
| Language | English |
| Publisher | Association for Computing Machinery (ACM) |
| Publisher Date | 1970-05-04 |
| Publisher Place | New York |
| Access Restriction | Subscribed |
| Content Type | Text |
| Resource Type | Article |
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