- Full text PDF available (5)
- This year (1)
- Last five years (3)
We formalize the algorithms computing primitive recursive (PR) functions as the abstract state machines (ASMs) whose running length is computable by a PR function. Then we show that there exists a programming language (implementing only PR functions) by which it is possible to implement any one of the previously defined algorithms for the PR functions in… (More)
In this paper we study the state complexity of catenation combined with symmetric difference. First, an upper bound is computed using some combinatoric tools. Then, this bound is shown to be tight by giving a witness for it. Moreover, we relate this work with the study of state complexity for two other combinations: catenation with union and catenation with… (More)
We improve some results relative to the state complexity of the multiple catenation described by Gao and Yu. In particular we nearly divide by 2 the size of the alphabet needed for witnesses. We also give some refinements to the algebraic expression of the state complexity, which is especially complex with this operation. We obtain these results by using… (More)
In this paper, we study the notion of code associated with the zigzag operation. After the recall of some results concerning codes and submonoids we give some deenitions about zigzag submonoids, zigzag codes, z-freeness and z-stability DLL93]. Then, we show some properties of z-free hulls of a given language and at last, we study the defect theorem which is… (More)
We exhaustively investigate possible combinations of a boolean operation together with a catenation. In many cases we prove and improve some conjectures by Brzozowski. For each family of operation, we endeavour to provide a common witness with a small size alphabet.