Realisable with Synchronous Communication (RSC)

• RSC is a framework that defines synchronous realisability in distributed specifications, ensuring deadlock-freedom and exact trace matching of projected components.
• It employs formal models such as communicating automata, global types, and control-state choreographies to capture semantic preservation under rendezvous communication.
• Decision procedures for RSC leverage conflict graph acyclicity and automata constructions, with complexity varying from PSPACE to 2-EXPTIME based on system characteristics.

Realisable with Synchronous Communication (RSC) denotes a class of semantic and algorithmic criteria for deciding whether a distributed specification is correctly implementable when communication is by synchronous rendez-vous. Across the formalisms represented in the literature—communicating automata, control-state choreographies, global types, and synchronous communicating state machines—the common core is that projected local components must realise exactly the behaviour prescribed by a global description under synchronous communication, typically together with deadlock-freedom. In adjacent automata-theoretic work, the same idea is expressed as synchronisability: asynchronous behaviours must be reorderable into behaviours in which each communication is effectively synchronous (Giusto et al., 5 Dec 2025, Li et al., 9 Feb 2026, Suresh et al., 4 Oct 2025).

1. Terminological scope and conceptual core

RSC is not a single syntactic formalism, but a family of closely aligned notions. In the multiparty-session and global-type literature, it is defined as deadlock-free realisability under synchronous communication. In control-state choreography work, the corresponding notion is language-synchronisability, and for stronger equivalence one also requires that every asynchronous trace can be continued to a stable one. In communicating-automata work, the term often appears as synchronisability or as the subclass of systems realisable with synchronous communication, characterised by the possibility of reordering asynchronous executions into rendez-vous witnesses (Schewe et al., 2020, Suresh et al., 4 Oct 2025).

The unifying theme is semantic preservation under projection. A global specification is projected onto local peers or local automata; the projected system is then executed under synchronous communication; and RSC asks whether the synchronous projected behaviour matches the intended global behaviour, without introducing deadlocks or spurious traces. In Li and Stutz’s formulation, an SCSM synchronously realizes a global protocol $G$ iff it satisfies protocol-fidelity, $L(\mathcal A)=L(G)$, and deadlock-freedom, meaning that no reachable configuration of $\mathcal A$ is a deadlock (Li et al., 9 Feb 2026).

An older antecedent appears in Witzel’s study of symmetric peer-to-peer systems in CSP. That work is not phrased in the terminology of RSC, but it isolates a closely related phenomenon: what synchronous communication can realise in a symmetric distributed system, especially when common knowledge must be attained without breaking topological symmetry. The paper shows that CSP with input and output guards can realise pairwise synchronisation symmetrically on peer-to-peer networks, whereas the restricted dialect with input-only guards cannot (0710.2284).

2. Formal models and canonical definitions

The literature gives several precise formulations of RSC-style properties.

Framework	Objects	Core requirement
Communicating automata	asynchronous trace $e$, communication $\Pi$	every execution has a causally equivalent i-RSC witness
Control-state choreographies	choreography $C$, projection $PP$	$L_0(C)=L_\omega(PP)$
Global types / MPST	global type $\gt$, projection $\proj{\gt}$	session-conformance plus deadlock-freedom in $L(\mathcal A)=L(G)$0
Synchronous protocols	global protocol $L(\mathcal A)=L(G)$1, SCSM $L(\mathcal A)=L(G)$2	$L(\mathcal A)=L(G)$3 and no reachable deadlock

For communicating automata, the 2025 unreliability study formalises channels as peer-to-peer FIFO links, actions as sends, receives, and internal $L(\mathcal A)=L(G)$4 actions, and configurations as control-state vectors paired with channel contents. In the synchronous abstraction, every send $L(\mathcal A)=L(G)$5 must match immediately with a receive $L(\mathcal A)=L(G)$6. An execution $L(\mathcal A)=L(G)$7 is i-RSC if every matching pair in $L(\mathcal A)=L(G)$8 is of the form $L(\mathcal A)=L(G)$9, and a system is i-RSC if every execution admits a causally equivalent i-RSC execution (Suresh et al., 4 Oct 2025).

For control-state choreographies, a CSC is a tuple $\mathcal A$0 whose transitions emit multisets of messages atomically under rendez-vous semantics. Its projection is a P2P system of control-state machines executed over p2p queues, per-receiver queues, or mailboxes. The choreography is language-synchronisable in semantics $\mathcal A$1 iff $\mathcal A$2, and it is synchronisable iff moreover every asynchronous trace can be continued to a stable one (Schewe et al., 2020).

For global types under synchronous communication, Di Giusto, Lozes, and Urso define RSC through two conditions. A global type $\mathcal A$3 is deadlock-free realisable under synchronous communication iff

$\mathcal A$4

and

$\mathcal A$5

Here deadlock-free in $\mathcal A$6 means that every finite prefix of a send/receive trace of $\mathcal A$7 can be extended to a complete accepting trace (Giusto et al., 5 Dec 2025).

The 2026 global-protocol formulation is closely related but uses a different semantic presentation. A global protocol is a deterministic, reduced DFA over the synchronous alphabet $\mathcal A$8, and synchronous realizability asks whether there exists some SCSM that realises the protocol with exact trace agreement and deadlock-freedom (Li et al., 9 Feb 2026).

3. Structural characterisations

A major line of work on RSC gives structural criteria that are equivalent to synchronous realisability.

In communicating automata, the central object is the conflict graph $\mathcal A$9, whose vertices are communication blocks and whose edges record precedence between non-commuting actions in distinct blocks. The key characterisation states that $e$0 is causally equivalent to an i-RSC execution iff $e$1 is acyclic. This turns RSC from a global trace-reordering question into an acyclicity condition over a finite dependency structure (Suresh et al., 4 Oct 2025).

In control-state choreographies, realisability is characterised by two combinatorial constraints. The sequence-condition constrains consecutive choreography transitions so that either the sender of the second message is one of the endpoints of the first, or the two messages can be swapped inside the corresponding transition-relations. The choice-condition constrains branching from the same control state so that either the two branches share a sender or each branch can be moved into the other transition-relation. The main theorem is that, for each buffer model $e$2, a finite CSC is realisable iff it satisfies both the sequence-condition and the choice-condition (Schewe et al., 2020).

For global types, session-conformance under synchronous communication admits an MSC characterisation. Proposition 16, specialised to $e$3, identifies the conformance requirement with inclusion of MSC languages generated by the projected CFSMs into the existential MSC language of the global type. This MSC view is then used to relate synchronous realisability to more asynchronous models. Theorem 22 states that if a global type is realisable under any communication model $e$4, then it is RSC. Theorem 23 gives a converse for causally-closed models, including peer-to-peer, bag, and causal ordering: realisability under $e$5 is equivalent to synchronous linearisability of all MSCs, orphan-freedom, deadlock-freedom under $e$6, and, in particular, RSC (Giusto et al., 5 Dec 2025).

The 2025 complementability study sharpens this picture for MPST. It proves that if a global type is deadlock-free realisable in $e$7, then it is deadlock-free realisable in $e$8. It also proves that synchronous realisability implies complementability: any global type realisable in the synchronous model admits a complementary global type describing the complement of its synchronous MSC behaviour (Giusto et al., 23 Jul 2025).

These results jointly position RSC as a semantic core. More permissive communication models may realise additional protocols, but whenever they realise a protocol correctly, the protocol is already correct under synchronous communication. The converse does not generally hold.

4. Decision procedures and complexity

RSC has been studied through several decision procedures, and the complexity bounds depend heavily on the formalism and on structural restrictions.

For communicating automata, the unreliability study reduces non-membership in i-RSC to emptiness of the intersection of two regular languages over a finite alphabet. One NFA, $e$9, recognises borderline violations and has size $\Pi$0. The other, $\Pi$1, recognises RSC prefixes and has size $\Pi$2, where $\Pi$3. The final emptiness test yields an overall decision procedure with complexity

$\Pi$4

This provides an explicit automata-theoretic algorithm for deciding i-RSC via conflict-graph acyclicity (Suresh et al., 4 Oct 2025).

For global types, Di Giusto, Lozes, and Urso give a PSPACE procedure for checking RSC when a complement automaton is available. The algorithm builds the pre-product NFA of the projected local CFSMs, intersects it with the complement of the global type, and checks emptiness to decide session-conformance; a separate reachability test ensures deadlock-freedom. If no explicit complement is given, complement construction may require a doubly exponential blow-up in the general case, pushing the overall procedure into EXPSPACE; for commutation-closed types, dualisation gives only linear blow-up (Giusto et al., 5 Dec 2025).

The complementability paper gives a related PSPACE result for deciding p2p realisability when both a global type $\Pi$5 and an explicit complement $\Pi$6 are given. The procedure checks four conditions: RSC, orphan-freedom, deadlock-freedom in $\Pi$7, and synchronous realisability. The synchronous conformance check again reduces to emptiness of an on-the-fly explored product NFA, and the overall procedure is PSPACE in $\Pi$8. For sender-driven choice, the paper also gives a complement construction with linear blow-up in the size of the global type (Giusto et al., 23 Jul 2025).

Li and Stutz establish a sharper frontier for global protocols under rendezvous synchrony. If the concurrency alphabet is transitive, synchronous realizability is decidable in 2-EXPTIME in the size of the protocol and in 3-EXPTIME in the size of the alphabet. If the global protocol is unambiguous, synchronous realizability is decidable in EXPTIME. In full generality, however, synchronous realizability of sink-final global protocols is undecidable. The same reductions also give the same complexity bounds for synchronous verification, where a candidate realization is part of the input (Li et al., 9 Feb 2026).

5. Communication models, topology, and robustness

A recurring conclusion is that the communication model affects realisability. Di Giusto, Lozes, and Urso state this explicitly: the communication model does not impact subtyping, but it impacts realisability. In their hierarchy, RSC is the simplest and most tractable core: if a global type is realisable under a model $\Pi$9, then it is RSC; conversely, stronger asynchrony may admit patterns that are not RSC (Giusto et al., 5 Dec 2025).

This dependence is also visible in synchronisability for communicating automata. Under mailbox semantics with arbitrary accepting states, synchronisability is undecidable. The proof reduces Post’s Correspondence Problem to a four-component network $C$0 such that asynchronous mailbox behaviour produces an accepting send-trace iff the PCP instance has a solution, while synchronous behaviour cannot reach the accepting state. By contrast, synchronisability is decidable for oriented ring topologies, and for directed tree topologies peer-to-peer and mailbox semantics coincide and synchronisability is decidable by a top-down computation of influenced languages. The all-states-accepting mailbox case for arbitrary topologies remains open (Giusto et al., 2024).

The 2025 unreliability study shows that standard RSC assumptions are fragile under failures. Two distinct failure models are considered: interference and crash-stop failures. For interference, the paper relaxes matching to i-matching, allowing differences in message value or order, and shows that the same NFAs $C$1 and $C$2 can be used over an enlarged action alphabet. The conflict-graph lemmas remain valid, and the overall PSPACE, even EXPTIME, complexity remains unchanged. For crash-stop failures, the paper introduces crash-handling communicating systems with three structural rules, CI, CP, and CR, and shows that the RSC test is unaffected by internal $C$3 and $C$4 actions because they do not introduce new cyclic dependencies in the conflict graph (Suresh et al., 4 Oct 2025).

The case studies in that paper further show that resilience is model-dependent. The benchmark “2-Paxos-2P-3A” still satisfies RSC and $C$5-MC under lossiness and out-of-order errors, but fails under message corruption when acceptors may mis-read. Tools mentioned include ReSCu, extended for interference, and kmc-checker, extended similarly (Suresh et al., 4 Oct 2025).

6. Symmetry, synchronous guards, and common knowledge

The older CSP analysis by Witzel clarifies a distinct but foundational aspect of synchronous communication: its role in obtaining common knowledge under symmetry constraints. A peer-to-peer network is defined there as a strongly connected, directly connected graph with at least two vertices and a non-trivial well-balanced automorphism. Pairwise synchronization means that every maximal computation is finite, properly terminates, and contains at least one direct communication between each pair of main processes. The positive theorem states that every such network admits a symmetric CSPi/o system that pairwise synchronizes all vertices. The negative theorem states that no symmetry-preserving extension admits a $C$6-symmetric CSPin system that pairwise synchronizes all main vertices, even when helper processes are added (0710.2284).

The distinction between CSPi/o and CSPin is exact. In CSPi/o, both input and output can occur inside guarded choice, so a process can wait symmetrically for either direction of rendez-vous and still avoid deadlock. In CSPin, outputs cannot appear in guards; two symmetric processes may therefore both choose unguarded output branches and deadlock. The paper’s failure example shows that adding helper buffers does not restore direct synchronous communication; pairwise synchronization is then lost, and with it the relevant common-knowledge effect (0710.2284).

This line of work suggests a useful historical interpretation of RSC. Later formulations focus on trace equivalence, MSC inclusion, automata products, and decidability, but the underlying issue is already present in the CSP setting: whether synchronous communication, under symmetry and without extra coordination, is strong enough to realise the intended distributed behaviour. A common misconception is that rendez-vous synchrony by itself removes implementability difficulties. The literature does not support that conclusion. Input-only guarded CSP remains too weak for symmetric pairwise synchronization, and general synchronous realizability is undecidable without structural restrictions (0710.2284, Li et al., 9 Feb 2026).

Taken together, these results place RSC at the intersection of semantics, concurrency theory, and verification. It is a correctness notion for projected implementations, a structural property of traces and MSCs, a decision problem with sharply varying complexity, and, in the presence of symmetry, a boundary on what synchronous communication can realise exactly.