Our Theory of Computation course covers finite automata (DFA and NFA), regular expressions and languages, the pumping lemma, context-free grammars and pushdown automata, Turing machines, decidability and an introduction to computational complexity. Lessons are live and one-to-one with a verified subject expert, who explains each concept with worked examples, solves problems from your own module and helps you prepare for exams and coursework. Suitable for computer science and engineering students, following university syllabi in the UK, US, Australia and India (including AKTU, VTU and Anna University style courses).
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In short: this course gives one-to-one online tutoring in theory of computation. A verified tutor explains automata, regular expressions, context-free grammars, pushdown automata, Turing machines and decidability, with step-by-step constructions and proofs.
Theory of Computation (TOC) is the branch of computer science that studies what problems can be solved by computers and how efficiently, using mathematical models of computation such as finite automata, pushdown automata and Turing machines. It covers formal languages and grammars, and the limits of computation, including undecidable problems.
This online course teaches Theory of Computation one to one with a verified tutor who has studied or taught it at university level, at your pace and aligned with your own module.
Related subject: Theory of computation help.
| Topic | Key content |
|---|---|
| Foundations | Alphabets, strings, languages, abstract machines |
| Regular languages | DFA, NFA, equivalence, minimisation, regular expressions, regular grammars |
| Properties of regular languages | Closure properties, decidability, pumping lemma |
| Context-free languages | Context-free grammars, derivations and parse trees, ambiguity, Chomsky and Greibach normal forms |
| Pushdown automata | Deterministic and non-deterministic PDA, equivalence with CFGs |
| Properties of CFLs | Closure properties, pumping lemma for CFLs |
| Turing machines | Design, variants, computable functions, Church–Turing thesis |
| Decidability | Recursive and recursively enumerable languages, the halting problem, reductions |
Use the subset construction.
Here is a typical question: design a DFA over {a, b} that accepts strings ending in ab.
| State | Meaning | On a | On b |
|---|---|---|---|
| q0 (start) | No useful suffix yet | q1 | q0 |
| q1 | Last symbol was a | q1 | q2 |
| q2 (accept) | String ends in ab | q1 | q0 |
Test: "aab" goes q0 → q1 → q1 → q2, so it is accepted.
Students most often lose marks in Theory of Computation through the habits below. Each is easy to fix with practice and feedback on your own answers.
| Mark-loser | What to do instead |
|---|---|
| Missing transitions in a DFA | Give every state a transition on every symbol |
| Pumping lemma misused | Choose the string carefully and cover every split |
| Ambiguous grammars unnoticed | Check for two parse trees |
| Closure properties misapplied | Recall which classes are closed under each operation |
| Decidability proofs unclear | State the reduction and its direction |
TOC modules are usually assessed by written exams with design questions (build a DFA, grammar or Turing machine), conversions and proofs, plus problem sheets.
Tutors explain concepts, work through practice problems with you and give feedback on your approach. Graded work you submit must be your own, as set out in our academic integrity policy. For deadline-driven guidance, see assignment help.
Lessons are live and one to one on video with screen sharing and a shared whiteboard. You can follow a full course or book sessions on the topics you find hardest before exams. See also Compiler Design, Design and Analysis of Algorithms and Discrete Structures.
A theory of computation tutor online gives you live 1-to-1 lessons on automata, grammars and Turing machines, designing machines with you step by step and practising the proofs your exam asks for.
This theory of computation course suits second- and third-year computer science students taking a TOC or automata theory module, and students preparing for competitive exams where automata and formal languages are tested.
Prerequisites: discrete mathematics, mathematical logic and basic set theory.
Course length: 40 one-hour lessons across 8 modules.
| Stage | Modules | What you can do afterwards |
|---|---|---|
| 1 | Abstract machines and formal languages, regular languages and finite automata | Design DFAs and NFAs and convert an NFA to a DFA |
| 2 | Properties of regular languages | Write regular expressions and use the pumping lemma |
| 3 | Context-free grammars, pushdown automata, properties of CFLs | Write CFGs, convert to normal forms and design PDAs |
| 4 | Turing machines, decidability | Design simple Turing machines and explain undecidable problems |
Where it leads: theory of computation is the foundation for our Compiler Design course and builds on Discrete Structures.
The study of what computers can compute, using models such as automata and Turing machines.
A DFA has exactly one move per state and symbol; an NFA can have several or none. Both recognise the same languages.
A property of regular (or context-free) languages used to prove a language is not in that class.
A set of rules that generate a language, where each rule replaces a single non-terminal.
A mathematical model of computation with an infinite tape, used to define what is computable.
The problem of deciding whether any program halts on an input; it is undecidable.
It is abstract, but practising constructions and proofs step by step makes it manageable.
Yes. Tutors practise automata design, conversions and proofs.
The price depends on the tutor and session length. You see the hourly rate before booking, with no subscription.
No. Tutors explain, guide and give feedback so you can complete your own work, in line with our academic integrity policy.
Use the subset construction: each DFA state is a set of NFA states.
TOC, theory of computation, is a core BTech computer science subject, usually taught in the second or third year. It studies abstract machines and the languages they accept: finite automata, regular expressions, context-free grammars, pushdown automata and Turing machines, ending with decidability. It prepares you for compiler design and algorithm theory.
No algorithm can decide the problem for every input, as with the halting problem.
Yes. Regular languages are a subset of context-free languages.
Decide what each state must remember, then define transitions for every symbol and test examples.
Not exactly. Automata theory, which studies finite automata, pushdown automata and Turing machines, is one major part of theory of computation. Theory of computation also covers computability, which asks what can be computed at all, and complexity theory, which studies how efficiently problems can be solved, including P and NP.
Yes. Lessons are online, so you can book times that suit your time zone.
Weekly lessons suit most students; add extra sessions before mocks and final exams.
Yes. You can book one session to see if the tutor suits you, with no subscription.
Two widely used textbooks are Introduction to the Theory of Computation by Michael Sipser and Introduction to Automata Theory, Languages, and Computation by Hopcroft, Motwani and Ullman. Many universities also set their own notes. Your tutor follows the book your module uses and adds exam-style automata questions.
Yes. You can learn with a 1-to-1 theory of computation tutor online through live lessons with a shared whiteboard. Your tutor designs DFAs, PDAs and Turing machines with you step by step, explains pumping lemma proofs and undecidability, and works through past-paper questions before your exam.
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