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Asymptotic cyclic expansion and bridge groups of formal proofs
 JOURNAL OF ALGEBRA
, 2001
"... Formal proofs, even simple ones, may hide an unexpected intricate combinatorics. We define a new combinatorial invariant, the bridge group of a proof, which encodes the cyclic structure of proofs in the sequent calculus. We compute the bridge groups of two infinite families of proofs and identify th ..."
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Cited by 5 (1 self)
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Formal proofs, even simple ones, may hide an unexpected intricate combinatorics. We define a new combinatorial invariant, the bridge group of a proof, which encodes the cyclic structure of proofs in the sequent calculus. We compute the bridge groups of two infinite families of proofs and identify them with the Baumslagâ€“Solitar and Gersten groups. We observe that the distortion of cyclic subgroups in these groups equals the asymptotic growth of the procedure of elimination of lemmas from the proofs.
On the form of witness terms
 ARCH. MATHEMATICAL LOGIC
, 2010
"... We investigate the development of terms during cutelimination in firstorder logic and Peano arithmetic for proofs of existential formulas. The form of witness terms in cutfree proofs is characterized in terms of structured combinations of basic substitutions. Based on this result, a regular tree ..."
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Cited by 4 (3 self)
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We investigate the development of terms during cutelimination in firstorder logic and Peano arithmetic for proofs of existential formulas. The form of witness terms in cutfree proofs is characterized in terms of structured combinations of basic substitutions. Based on this result, a regular tree grammar computing witness terms is given and a class of proofs is shown to have only elementary cutelimination.
The Cost of a Cycle is a Square
, 1999
"... The logical flow graphs of sequent calculus proofs might contain oriented cycles. For the predicate calculus the elimination of cycles might be nonelementary and this was shown in [Car96]. For the propositional calculus, we prove that if a proof of k lines contains n cycles then there exists an ..."
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Cited by 3 (2 self)
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The logical flow graphs of sequent calculus proofs might contain oriented cycles. For the predicate calculus the elimination of cycles might be nonelementary and this was shown in [Car96]. For the propositional calculus, we prove that if a proof of k lines contains n cycles then there exists an acyclic proof with O(k n+1 ) lines. In particular, there is a quadratic time algorithm which eliminates a single cycle from a proof. These results are motivated by the search for general methods on proving lower bounds on proof size and by the design of more efficient heuristic algorithms for proof search.
Streams and strings of formal proofs
 Theoretical Computer Science
, 2000
"... www.elsevier.com/locate/tcs ..."
Streams and Strings in Formal Proofs
"... Streams are acyclic directed subgraphs of the logical flow graph of a proof and represent bundles of paths with the same origin and the same end. Streams can be described with a natural algebraic formalism which allows to explain in algebraic terms the evolution of proofs during cutelimination. ..."
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Streams are acyclic directed subgraphs of the logical flow graph of a proof and represent bundles of paths with the same origin and the same end. Streams can be described with a natural algebraic formalism which allows to explain in algebraic terms the evolution of proofs during cutelimination. In our approach, "logic" is often forgotten and combinatorial properties of graphs are taken into account to explain logical phenomena.