### Table 1: Interaction styles for proof step articulation

1996

Cited by 2

### Table 1 The complexity of some interactive proofs. fi are superpolynomial functions and g is an increasing function (at in nity).

"... In PAGE 5: ... 2 3.3 Discussion In Table1 we survey the performance of our scheme compared to previous ones that are similar. We rst compare our protocol with Burmester apos;s version of the Guillou-Quisquater one.... ..."

### Table 1: The Chemistry / Proof-Theory Roadmap

"... In PAGE 41: ...Table1 : The Chemistry / Proof-Theory Roadmap (continued) chemistry -calculus Linear logic duality (dualities apparent in stereo- chemical complementarity, hy- drophilic/hydrophobic, proton donor/acceptor, reductant/oxidant) | duality (linear negation is involutive, de ned by DeMorgan duali- ties) symmetry (reactive interaction is sym- metric) asymmetric (functional application is not commutative) symmetric (assumption and conclusion are dual - i.e.... ..."

### Table 1: The Chemistry / Proof-Theory Roadmap

"... In PAGE 41: ...Table1 : The Chemistry / Proof-Theory Roadmap (continued) chemistry -calculus Linear logic duality (dualities apparent in stereo- chemical complementarity, hy- drophilic/hydrophobic, proton donor/acceptor, reductant/oxidant) | duality (linear negation is involutive, de ned by DeMorgan duali- ties) symmetry (reactive interaction is sym- metric) asymmetric (functional application is not commutative) symmetric (assumption and conclusion are dual - i.e.... ..."

### Table 1: The Chemistry / Proof-Theory Roadmap (continued)

"... In PAGE 40: ...Table1 : The Chemistry / Proof-Theory Roadmap Chemistry -calculus Linear logic molecule as physical object (the nature of atoms and their bonds) -term in normal form proof-net in normal form (multiplicative fragment of lin- ear logic) shape as action (domain of interaction) (with whom and how a molecule interacts, as deter- mined by its shape and the na- ture of its reactive groups) type (speci cation of an action: a description of what the term does at a particular level of res- olution) multiset of propositional formulae (theorem) (a set of \actionable quot; ad- dresses, \interfaces quot;, or \plug- ging speci cations quot;) bonds (connectors of molecular parts) abstraction and application left and right rules of logical connectives initiation of a reaction application rule of inference: cut (reactants are the premises, products are the conclusions) completion of a reaction (structural rearrangements into stable products) normalization cut elimination branching reaction (multiple reaction pathways among the reactants) | multiple cut options (a sequent is a multiset) synthesis pathway (representation of a molecule as a suite of reactions between intermediates which enable its synthesis) -term containing redexes proof-net with cut(s) (a proof making use of inter- mediate results { lemmas a.k.... ..."

### Table 1: The Chemistry / Proof-Theory Roadmap (continued)

"... In PAGE 40: ...Table1 : The Chemistry / Proof-Theory Roadmap Chemistry -calculus Linear logic molecule as physical object (the nature of atoms and their bonds) -term in normal form proof-net in normal form (multiplicative fragment of lin- ear logic) shape as action (domain of interaction) (with whom and how a molecule interacts, as deter- mined by its shape and the na- ture of its reactive groups) type (speci cation of an action: a description of what the term does at a particular level of res- olution) multiset of propositional formulae (theorem) (a set of \actionable quot; ad- dresses, \interfaces quot;, or \plug- ging speci cations quot;) bonds (connectors of molecular parts) abstraction and application left and right rules of logical connectives initiation of a reaction application rule of inference: cut (reactants are the premises, products are the conclusions) completion of a reaction (structural rearrangements into stable products) normalization cut elimination branching reaction (multiple reaction pathways among the reactants) | multiple cut options (a sequent is a multiset) synthesis pathway (representation of a molecule as a suite of reactions between intermediates which enable its synthesis) -term containing redexes proof-net with cut(s) (a proof making use of inter- mediate results { lemmas a.k.... ..."

### lable. Proof:

2000

Cited by 1

### Table 1. Representative performance comparison of proof search in the implementa- tions of the systems BVu, BVi, BVu0 and BVi0.

"... In PAGE 40: ... crl [q43-down] : [ lt; U ; V gt; , lt; R ; T gt; ] = gt; lt; R ; [ T , lt; U ; V gt; ] gt; if T ci lt; U ; V gt; = can-interact . endm Table1 gives a performance comparison of the implementations of the sys- tems that we discussed so far in this chapter with the performance of the system BV. These experiments were performed on the following structures: 1.... ..."