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This problem examines whether the following specifications are satisfiable: 1. If the file system is not locked, then (a) new messages will be queued. (b) new messages will be sent to the messages buffer. (c) the system is functioning normally, and conversely, if the system is functioning normally, then the file system is not locked. 2. If new messages are not queued, then they will be sent to the messages buffer. 3. New messages will not be sent to the message buffer. (a) Begin by translating the five specifications into propositional formulas using four propositional variables: L::= file system locked, Q::= new messages are queued, B ::= new messages are sent to the message buffer, N ::= system functioning normally. (b) Demonstrate that this set of specifications is satisfiable by describing a single truth assignment for the variables L, Q, B, N and verifying that under this assign- ment, all the specifications are true. (c) Argue that the assignment determined in part (b) is the only one that does the job.

This problem examines whether the following specifications are satisfiable: 1. If the file system is not locked, then (a) new messages will be queued. (b) new messages will be sent to the messages buffer. (c) the system is functioning normally, and conversely, if the system is functioning normally, then the file system is not locked. 2. If new messages are not queued, then they will be sent to the messages buffer. 3. New messages will not be sent to the message buffer. (a) Begin by translating the five specifications into propositional formulas using four propositional variables: L::= file system locked, Q::= new messages are queued, B ::= new messages are sent to the message buffer, N ::= system functioning normally. (b) Demonstrate that this set of specifications is satisfiable by describing a single truth assignment for the variables L, Q, B, N and verifying that under this assign- ment, all the specifications are true. (c) Argue that the assignment determined in part (b) is the only one that does the job.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Discrete Math Sets and proofs
This problem examines whether the following specifications are satisfiable: 1. If the file system is not locked, then (a) new messages will be queued. (b) new messages will be sent to the messages buffer. (c) the system is functioning normally, and conversely, if the system is functioning normally, then the file system is not locked. 2. If new messages are not queued, then they will be sent to the messages buffer. 3. New messages will not be sent to the message buffer. (a) Begin by translating the five specifications into propositional formulas using four propositional variables: L: file system locked, Q::= new messages are queued, B::= new messages are sent to the message buffer, N := system functioning normally. (b) Demonstrate that this set of specifications is satisfiable by describing a single truth assignment for the variables L, Q, B, N and verifying that under this assign- ment, all the specifications are true. (c) Argue that the assignment determined in part (b) is the only one that does the job.
Transcribed Image Text:This problem examines whether the following specifications are satisfiable: 1. If the file system is not locked, then (a) new messages will be queued. (b) new messages will be sent to the messages buffer. (c) the system is functioning normally, and conversely, if the system is functioning normally, then the file system is not locked. 2. If new messages are not queued, then they will be sent to the messages buffer. 3. New messages will not be sent to the message buffer. (a) Begin by translating the five specifications into propositional formulas using four propositional variables: L: file system locked, Q::= new messages are queued, B::= new messages are sent to the message buffer, N := system functioning normally. (b) Demonstrate that this set of specifications is satisfiable by describing a single truth assignment for the variables L, Q, B, N and verifying that under this assign- ment, all the specifications are true. (c) Argue that the assignment determined in part (b) is the only one that does the job.
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