A Non-geometric Switch Toggling Problem
نویسنده
چکیده
Switch toggling games such as Lights Out and the σ-game are widely studied in mathematics and have been applied to model a variety of situations such as genetic networks and cellular automata. This paper introduces a class of toggling games where at each iteration a fixed number of switches is chosen to be toggled where the only switches changed are the switches chosen to be toggled. The switches all operate independently of each other and do not depend on the proximity or the position relative to any other switch. This paper classifies the conditions necessary and the steps taken to transition from all switches in the on state to all switches in the off state. Further results include the conditions required of the parity between the number of switches in the system and the fixed number of switches toggled at each step in order to transition from a given initial state to a specified terminal state. Acknowledgements: I would like to thank Dr. Richard Daquila for all of his help and support during this project as a part of the Muskie Fellowship program at Muskingum University. I would also like to thank Rose-Hulman Undergraduate Math Journal for giving me this opportunity as well as my parents for their continued love and support. Page 60 RHIT Undergrad. Math. J., Vol. 14, no. 2
منابع مشابه
Machine Repair Queueing System with with Non-Reliable Service Stations And Heterogeneous Service Discipline (RESEARCH NOTE)
This investigation deals with M/M/R/N machine repair problem with R non-reliable service stations which are subjected to unpredictable breakdown. 1here is provision of an additional server to reduce backlog in the case of heavy load of failed machines. 1he permanent service stations repair the failed machines at an identical rate m and switch to faster repair rate when all service stations are ...
متن کاملUsing well-solvable minimum cost exact covering for VLSI clock energy minimization
To save energy of VLSI systems flip-flops (FFs) are grouped in Multi-Bit Flip-Flop (MBFF), sharing a common clock driver. The energy savings strongly depends the grouping. For 2-bit MBFFs the optimal grouping turns into a minimum cost perfect graph matching problem. For k-bit MBFFs the optimal grouping turns into a minimum cost exact k-covering problem. We show that due to their special setting...
متن کاملA Tool for Answering Queries on Action Descriptions
Action languages [1] are a formal tool for reasoning about actions, where an agent’s knowledge about a domain in question is represented by a declarative action description that consists of logical formulas. For instance, consider a light bulb with a switch. When the light is off, then toggling the switch turns the light on; this can be expressed in the action description language C [2] by the ...
متن کاملPosynomial geometric programming problem subject to max–product fuzzy relation equations
In this article, we study a class of posynomial geometric programming problem (PGPF), with the purpose of minimizing a posynomial subject to fuzzy relational equations with max–product composition. With the help of auxiliary variables, it is converted convert the PGPF into an equivalent programming problem whose objective function is a non-decreasing function with an auxiliary variable. Some pr...
متن کاملToggling a Genetic Switch Using Reinforcement Learning
In this paper, we consider the problem of optimal exogenous control of gene regulatory networks. Our approach consists in adapting an established reinforcement learning algorithm called the fitted Q iteration. This algorithm infers the control law directly from the measurements of the system’s response to external control inputs without the use of a mathematical model of the system. The measure...
متن کامل