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Journal Articles Theory of Computing Systems Year : 2002

On the mortality problem for matrices of low dimensions

Abstract

In this paper, we discuss the existence of an algorithm to decide if a given set of $2 × 2$ matrices is mortal. A set $F=s ¼,A_ms>$ of square matrices is said to be \motnouv{mortal} if there exist an integer $k >³ 1$ and some integers $i_1,i_2,>¼,i_k >Î s <1, >¼, ms>$ with $A_{i_1} A_{i_2} s~ A_{i_k}=0$. We survey this problem and propose some new extensions. We prove the problem to be BSS-undecidable for real matrices and Turing-decidable for two rational matrices. We relate the problem for rational matrices to the entry-equivalence problem, to the zero-in-the-corner problem, and to the reachability problem for piecewise-affine functions. Finally, we state some NP-completeness results.

Dates and versions

inria-00100725 , version 1 (26-09-2006)

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Olivier Bournez, Michael Branicky. On the mortality problem for matrices of low dimensions. Theory of Computing Systems, 2002, 35 (4), pp.433-448. ⟨10.1007/s00224-002-1010-5⟩. ⟨inria-00100725⟩
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