### Abstract

This paper is on the foundations of a recent approach to the design of massively parallel and interactive programming languages using rv-systems (interactive systems with registers and voices) and Agapia programming. It includes a few theoretical results on FISs (finite interactive systems), the underlying mechanism used for specifying control and interaction in these systems. First, we give a proof for the undecidability of the emptiness problem for FISs by reduction to the Post Correspondence Problem. Next, we use the proof to get other undecidability results, e.g., for the accessibility of a transition in a FIS, or for the finiteness of the language recognized by a FIS. Finally, we present a simple proof of the equivalence between FISs and tile systems, making explicit that they precisely capture recognizable two-dimensional languages.

Original language | English |
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Title of host publication | Proceedings of the 2008 10th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2008 |

Pages | 366-369 |

Number of pages | 4 |

DOIs | |

Publication status | Published - 2008 |

Externally published | Yes |

Event | 2008 10th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2008 - Timisoara Duration: Sep 26 2008 → Sep 29 2008 |

### Other

Other | 2008 10th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2008 |
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City | Timisoara |

Period | 9/26/08 → 9/29/08 |

### Fingerprint

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Software

### Cite this

*Proceedings of the 2008 10th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2008*(pp. 366-369). [5204840] https://doi.org/10.1109/SYNASC.2008.42

**Undecidability results for finite interactive systems.** / Sofronia, Alexandru; Popa, Alexandru; Stefanescu, Gheorghe.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 2008 10th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2008.*, 5204840, pp. 366-369, 2008 10th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2008, Timisoara, 9/26/08. https://doi.org/10.1109/SYNASC.2008.42

}

TY - GEN

T1 - Undecidability results for finite interactive systems

AU - Sofronia, Alexandru

AU - Popa, Alexandru

AU - Stefanescu, Gheorghe

PY - 2008

Y1 - 2008

N2 - This paper is on the foundations of a recent approach to the design of massively parallel and interactive programming languages using rv-systems (interactive systems with registers and voices) and Agapia programming. It includes a few theoretical results on FISs (finite interactive systems), the underlying mechanism used for specifying control and interaction in these systems. First, we give a proof for the undecidability of the emptiness problem for FISs by reduction to the Post Correspondence Problem. Next, we use the proof to get other undecidability results, e.g., for the accessibility of a transition in a FIS, or for the finiteness of the language recognized by a FIS. Finally, we present a simple proof of the equivalence between FISs and tile systems, making explicit that they precisely capture recognizable two-dimensional languages.

AB - This paper is on the foundations of a recent approach to the design of massively parallel and interactive programming languages using rv-systems (interactive systems with registers and voices) and Agapia programming. It includes a few theoretical results on FISs (finite interactive systems), the underlying mechanism used for specifying control and interaction in these systems. First, we give a proof for the undecidability of the emptiness problem for FISs by reduction to the Post Correspondence Problem. Next, we use the proof to get other undecidability results, e.g., for the accessibility of a transition in a FIS, or for the finiteness of the language recognized by a FIS. Finally, we present a simple proof of the equivalence between FISs and tile systems, making explicit that they precisely capture recognizable two-dimensional languages.

UR - http://www.scopus.com/inward/record.url?scp=70449492714&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449492714&partnerID=8YFLogxK

U2 - 10.1109/SYNASC.2008.42

DO - 10.1109/SYNASC.2008.42

M3 - Conference contribution

AN - SCOPUS:70449492714

SN - 9780769535234

SP - 366

EP - 369

BT - Proceedings of the 2008 10th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2008

ER -