Provable Coordination for LLM Agents via Message Sequence Charts

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• is either the agreed verdict or the conservative fallbackunknown. 7 Conclusion We presented a domain-specific language for multi-agent LLM coordination based on message sequence charts, together with a syntax-directed projection that derives correct local programs from a global workflow specificationclaim 82%
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  is either the agreed verdict or the conservative fallbackunknown. 7 Conclusion We presented a domain-specific language for multi-agent LLM coordination based on message sequence charts

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• Message Sequence Charts Benedikt Bollig1[0000-0003-0985-6115], Matthias F¨ ugger1[0000-0001-5765-0301], and Thomas Nowak1,2[0000-0003-1690-9342] 1 Universit´ e Paris-Saclay, CNRS, ENS Paris-Saclay, LMF, Gif-sur-Yvette, France 2 Institut Universitaire de France, Paris, France Abstractclaim 82%
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  Message Sequence Charts Benedikt Bollig1[0000-0003-0985-6115], Matthias F¨ ugger1[0000-0001-5765-0301], and Thomas Nowak1,2[0000-0003-1690-9342] 1 Universit´ e Paris-Saclay, CNRS, ENS Paris-Saclay, LMF, Gif-sur-Yvette

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• x,yA B x,y Fig. 2.Canonical one-step MSCs used in Definition 7. The schematic figure shows the empty MSC, a local choice event, a local action event, and a single message exchange. Table 1.Inductive MSC semantics of global workflows. JεK={M ε} JmsgA(x)→B(y)K={M A→B x,y } JactA:y=f(x)K={M A,f x,y }claim 82%
  Evidencepartial

  x,yA B x,y Fig. 2.Canonical one-step MSCs used in Definition 7. The schematic figure shows the empty MSC, a local choice event, a local action event, and a single message exchange. Table 1

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• Jifc@BthenP ⊤ elseP ⊥K={M B if⊤(c@B) ◦M|M∈JP ⊤K} ∪{M B if⊥(c@B) ◦M|M∈JP ⊥K} Jwhilec@BdoP body exitP exit K= S k≥0    M⊤ 1 ◦ ··· ◦M⊤ k ◦M ⊥ exit |claim 82%
  Evidencepartial

  Jifc@BthenP ⊤ elseP ⊥K={M B if⊤(c@B) ◦M|M∈JP ⊤K} ∪{M B if⊥(c@B) ◦M|M∈JP ⊥K} Jwhilec@BdoP body exitP exit K= S k≥0    M⊤ 1 ◦ ··· ◦M⊤ k ◦M ⊥ exit |

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• Mexit ∈JP exit K    whereM ⊤ i =M B while⊤(c@B) ◦M i andM ⊥ exit =M B while⊥(c@B) ◦M exit . Definition 8 (Inductive MSC Semantics).The semanticsJPKof a well- typed global workflowPis a set of MSCs. It is defined by structural recursion with the rules given in Table 1claim 82%
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  Mexit ∈JP exit K    whereM ⊤ i =M B while⊤(c@B) ◦M i andM ⊥ exit =M B while⊥(c@B) ◦M exit . Definition 8 (Inductive MSC Semantics).The semanticsJPKof a well- typed global workflowPis a set of MSCs

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• rather than from a global workflow directly. ForS∈LocProg A, we define⟨ ⟨S⟩ ⟩ ⊆Σ∗ A, the set of local traces ofS, by induction. The receive-guarded control constructsif/whileA(y)←Bconsume control-tagged messages fromBand branch on the first component (⊤or⊥). The formal definition is given in Table 2; thereclaim 82%
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  rather than from a global workflow directly. ForS∈LocProg A, we define⟨ ⟨S⟩ ⟩ ⊆Σ∗ A, the set of local traces ofS, by induction

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• M= (w A)A∈L wA ∈ ⟨ ⟨SA⟩ ⟩for allA, Mis a complete MSCclaim 82%
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  M= (w A)A∈L wA ∈ ⟨ ⟨SA⟩ ⟩for allA, Mis a complete MSC

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