On the decidability and complexity of problems for restricted hierarchical hybrid systems

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• 作者：Paul C. Bell^a ; ^{P.Bell@lboro.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Shang Chen^a ; ^{S.Chen3@lboro.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Lisa Jackson^b ; ^{L.M.Jackson@lboro.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Hybrid systems ; Reachability and mortality ; Piecewise affine maps ; (Hierarchical) piecewise constant derivatives
• 刊名：Theoretical Computer Science
• 出版年：2016
• 出版时间：1 November 2016
• 年：2016
• 卷：652
• 期：Complete
• 页码：47-63
• 全文大小：672 K

文摘

We study variants of a recently introduced hybrid system model, called a Hierarchical Piecewise Constant Derivative (HPCD). These variants (loosely called Restricted HPCDs) form a class of natural models with similarities to many other well known hybrid system models in the literature such as Stopwatch Automata, Rectangular Automata and PCDs. We study the complexity of reachability and mortality problems for variants of RHPCDs and show a variety of results, depending upon the allowed powers. These models form a useful tool for the study of the complexity of such problems for hybrid systems, due to their connections with existing models.

We show that the reachability problem and the mortality problem are co-NP-hard for bounded 3-dimensional RHPCDs (3-RHPCDs). Reachability is shown to be in PSPACE, even for n-dimensional RHPCDs. We show that for an unbounded 3-RHPCD, the reachability and mortality problems become undecidable. For a nondeterministic variant of 2-RHPCDs, the reachability problem is shown to be PSPACE-complete.