Automatic Theorem-Proving in Combinatorics on Words
نویسندگان
چکیده
We describe a technique for mechanically proving certain kinds of theorems in combinatorics on words, using automata and a package for manipulating them. We illustrate our technique by solving, purely mechanically, an open problem of Currie and Saari on the lengths of unbordered factors in the Thue-Morse sequence. Dedicated to the memory of Sheng Yu (1950–2012): friend and colleague
منابع مشابه
Automatic Theorem Proving in Walnut
2 Basics 3 2.1 Words and Automata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Number Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Automatic Words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
متن کاملOn the number of Abelian Bordered Words (with an Example of Automatic Theorem-Proving)
In the literature, many bijections between (labeled) Motzkin paths and various other combinatorial objects are studied. We consider abelian (un)bordered words and show the connection with irreducible symmetric Motzkin paths and paths in Z not returning to the origin. This study can be extended to abelian unbordered words over an arbitrary alphabet and we derive expressions to compute the number...
متن کاملA short introduction to two approaches in formal verification of security protocols: model checking and theorem proving
In this paper, we shortly review two formal approaches in verification of security protocols; model checking and theorem proving. Model checking is based on studying the behavior of protocols via generating all different behaviors of a protocol and checking whether the desired goals are satisfied in all instances or not. We investigate Scyther operational semantics as n example of this...
متن کاملA shortest single axiom with neutral element for commutative Moufang loops of exponent 3
In this brief note, we exhibit a shortest single product and neutral element axiom for commutative Moufang loops of exponent 3 that was found with the aid of the automated theorem-prover Prover9.
متن کاملProof-Checking, Theorem-Proving, and Program Verification
This article consists of three parts: a tutorial introduction to a computer program that proves theorems by induction; a brief description of recent applications of that theorem-prover; and a discussion of several nontechnical aspects of the problem of building automatic theorem-provers. The theorem-prover described has proved theorems such as the uniqueness of prime factorizations, Fermat’s th...
متن کامل