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The Automated Mathematician (AM) is one of the earliest successful discovery systems. [1] It was created by Douglas Lenat in Lisp, [2] and in 1977 led to Lenat being awarded the IJCAI Computers and Thought Award.
Automata are often classified by the class of formal languages they can recognize, as in the Chomsky hierarchy, which describes a nesting relationship between major classes of automata. Automata play a major role in the theory of computation , compiler construction , artificial intelligence , parsing and formal verification .
The quality of implemented systems has benefited from the existence of a large library of standard benchmark examples—the Thousands of Problems for Theorem Provers (TPTP) Problem Library [25] —as well as from the CADE ATP System Competition (CASC), a yearly competition of first-order systems for many important classes of first-order problems.
Automated reasoning programs are being applied to solve a growing number of problems in formal logic, mathematics and computer science, logic programming, software and hardware verification, circuit design, and many others. The TPTP (Sutcliffe and Suttner 1998) is a library of such problems that is updated on a regular basis.
ACL2 – a programming language, a first-order logical theory, and a theorem prover (with both interactive and automatic modes) in the Boyer–Moore tradition.; Coq – Allows the expression of mathematical assertions, mechanically checks proofs of these assertions, helps to find formal proofs, and extracts a certified program from the constructive proof of its formal specification.
Automath ("automating mathematics") is a formal language, devised by Nicolaas Govert de Bruijn starting in 1967, for expressing complete mathematical theories in such a way that an included automated proof checker can verify their correctness.