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Word equations over graph products
 In Proceedings of the 23rd Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2003), Mumbai (India), number 2914 in Lecture Notes in Computer Science
, 2003
"... For monoids that satisfy a weak cancellation condition, it is shown that the decidability of the existential theory of word equations is preserved under graph products. Furthermore, it is shown that the positive theory of a graph product of groups can be reduced to the positive theories of those fac ..."
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Cited by 13 (8 self)
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For monoids that satisfy a weak cancellation condition, it is shown that the decidability of the existential theory of word equations is preserved under graph products. Furthermore, it is shown that the positive theory of a graph product of groups can be reduced to the positive theories of those factors, which commute with all other factors, and the existential theories of the remaining factors. Both results also include suitable constraints for the variables. Larger classes of constraints lead in many cases to undecidability results.
Logical Aspects of CayleyGraphs: The Group Case
 TO APPEAR IN ANNALS OF PURE AND APPLIED LOGIC
"... We prove that a finitely generated group is contextfree whenever its Cayleygraph has a decidable monadic secondorder theory. Hence, by the seminal work of Muller and Schupp, our result gives a logical characterization of contextfree groups and also proves a conjecture of Schupp. To derive this re ..."
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Cited by 12 (3 self)
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We prove that a finitely generated group is contextfree whenever its Cayleygraph has a decidable monadic secondorder theory. Hence, by the seminal work of Muller and Schupp, our result gives a logical characterization of contextfree groups and also proves a conjecture of Schupp. To derive this result, we investigate general graphs and show that a graph of bounded degree with a high degree of symmetry is contextfree whenever its monadic secondorder theory is decidable. Further, it is shown that the word problem of a finitely generated group is decidable if and only if the firstorder theory of its Cayleygraph is decidable.
Existential and Positive Theories of Equations in Graph Products
 Theory of Computing Systems
, 2003
"... We prove that the existential theory of equations with normalized rational constraints in a fixed graph product of finite monoids, free monoids, and free groups is PSPACEcomplete. Under certain restrictions this result also holds if the graph product is part of the input. As the second main resu ..."
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Cited by 7 (6 self)
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We prove that the existential theory of equations with normalized rational constraints in a fixed graph product of finite monoids, free monoids, and free groups is PSPACEcomplete. Under certain restrictions this result also holds if the graph product is part of the input. As the second main result we prove that the positive theory of equations with recognizable constraints in graph products of finite and free groups is decidable.