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<p>An algorithm that decides the uniform word problem for lattices is given and shown to have <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(O(n^3)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>n</mi> <mn>3</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> running-time, which also gives an <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(O(n^3)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>n</mi> <mn>3</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> algorithm for the quasi-equational theory of lattices. This result continues a long sequence of algorithms for this problem, starting with Skolem in 1920. The algorithm makes use of Cosmadakis’ algorithm for the uniform word problem and Freese’s algorithm for the word problem for free lattices.</p>

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On the uniform word problem for lattices

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月3日

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  • C. J. Van Alten

摘要

An algorithm that decides the uniform word problem for lattices is given and shown to have \(O(n^3)\) O ( n 3 ) running-time, which also gives an \(O(n^3)\) O ( n 3 ) algorithm for the quasi-equational theory of lattices. This result continues a long sequence of algorithms for this problem, starting with Skolem in 1920. The algorithm makes use of Cosmadakis’ algorithm for the uniform word problem and Freese’s algorithm for the word problem for free lattices.