scholarly journals Reachability in Two-Dimensional Vector Addition Systems with States Is PSPACE-Complete

2015 ◽  
Author(s):  
Michael Blondin ◽  
Alain Finkel ◽  
Stefan Goller ◽  
Christoph Haase ◽  
Pierre McKenzie
Keyword(s):  
Two Dimensional ◽  
Dimensional Vector ◽  
Vector Addition

scholarly journals The Reachability Problem for Two-Dimensional Vector Addition Systems with States

2021 ◽  
Vol 68 (5) ◽  
pp. 1-43
Author(s):  
Michael Blondin ◽  
Matthias Englert ◽  
Alain Finkel ◽  
Stefan GÖller ◽  
Christoph Haase ◽  
...  
Keyword(s):  
Regular Expression ◽  
Two Dimensional ◽  
Dimensional Vector ◽  
Reachability Problem ◽  
Technical Result ◽  
Vector Addition ◽  
Bounded Language

We prove that the reachability problem for two-dimensional vector addition systems with states is NL-complete or PSPACE-complete, depending on whether the numbers in the input are encoded in unary or binary. As a key underlying technical result, we show that, if a configuration is reachable, then there exists a witnessing path whose sequence of transitions is contained in a bounded language defined by a regular expression of pseudo-polynomially bounded length. This, in turn, enables us to prove that the lengths of minimal reachability witnesses are pseudo-polynomially bounded.

scholarly journals Students’ Understanding of Graphical Vector Addition in One and Two Dimensions

2011 ◽  
Vol 3 (2) ◽  
pp. 102-111
Author(s):  
Umporn Wutchana ◽  
Narumon Emarat
Keyword(s):  
High School ◽  
High School Students ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Dimensional Vector ◽  
School Students ◽  
Free Response ◽  
Vector Addition ◽  
Qualitative Understanding ◽  
Graphical Vector

Understanding initial topics in physics (forces, fields, and kinematical quantities) requires a grasp of basic vector concepts. In this study, we intended to explore students’ qualitative understanding of graphical vector addition in one and two dimensions. Using two free-response problems of a diagnostic quiz, one is one-dimensional vector addition and the other is two-dimensional vector addition. Sixty-three grade ten high-school students’ responses were categorized. From the investigation, results represent that from the high-school students who already completed their vector lesson, only 10% of them provided correct answer for vector addition in one-dimension and 32% for the two-dimensional addition.

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