Fundamental question: what problems can we solve with a computer?

Automata

• an automaton (plural: automata) is a mathematical model of a computing device
• an abstraction of a real computer, the way that graphs are abstractions of social networks, transportation grids, etc.

an example: calculators vs. desktops

• calculators: small amount of memory, desktop: large amount of memory
• calculators: fixed set of functions, desktop: reprogrammable, run many different programs
• in CS 103, we’ll first explore “small-memory” computers, then discuss “large-memory” computers

what’s in common in computing devices

• e.g. four-function calculator vs. abacus
• these machines receive input from an external source
• input is provided sequentially, one discrete unit at a time
• each input causes the devices to change configuration

modeling finite computation → finite automaton (plural: finite automata)

We’ll model a finite-memory computer as a collection of states linked by transitions

• each state corresponds to one possible configuration of the device’s memory, and each transition indicates how memory changes in response to inputs
• let each transition be labelled by a character
• now, a set of inputs is just a string made of characters
  • start from start state
  • change state depending on character
• as a simplifying assumption, assume that we just need to get a single bit of output. our machines will just say YES or NO. (this can be generalized)