Tiga in Research: Diverse Contexts

• Tiga is a term used in multiple research domains, serving as a local identifier with meanings that vary from quantum entanglement measures to verification tools and transaction protocols.
• In quantum information, Tiga refers to the three-tangle measure that distinguishes GHZ- and W-type entanglements through convex-roof extensions and periodic phase analysis.
• In systems verification and distributed databases, Tiga underpins methods for timed-game analysis, worst-case execution time calculations, and 1-WRTT geo-transaction processing with robust fault tolerance.

Searching arXiv for recent and canonical uses of “Tiga” across domains to ground the article. “Tiga” is not a single technical object in the arXiv literature surveyed here. It designates, in different research communities, a multipartite entanglement measure interpreted as the three-tangle, a named external pilot trial in child mental health, the timed-game verifier UPPAAL-TiGA, an extended symbolic verification line positioned relative to that tool, and a geo-distributed transaction protocol for strictly serializable databases (Ma et al., 2013, Wilson et al., 2019, Cassez, 2010, Jensen et al., 9 Jun 2025, Geng et al., 6 Sep 2025). The term is therefore best understood contextually: its meaning is determined by the surrounding field, formalism, and problem setting.

1. Distinct research uses of the term

In the sources considered here, “Tiga” appears in four technically unrelated domains. The commonality is lexical rather than methodological.

Use of “Tiga”	Research context	Representative paper
Three-tangle	Tripartite entanglement of three-qubit mixed states	(Ma et al., 2013)
TIGA-CUB	External pilot trial assessing feasibility of a definitive trial	(Wilson et al., 2019)
UPPAAL-TiGA	Timed-game verification and WCET computation	(Cassez, 2010)
Tiga	Geo-distributed transactional database protocol	(Geng et al., 6 Sep 2025)

A further development appears in timed verification: an on-the-fly symbolic algorithm for timed alternating-time temporal logic is presented explicitly relative to Uppaal Tiga, extending and generalizing its style of symbolic game verification while also reporting a performance improvement after porting a new abstraction back into Tiga (Jensen et al., 9 Jun 2025).

This dispersion of meaning matters because identical terminology otherwise risks conflating unrelated constructs: an entanglement monotone, a clinical-trial acronym, a real-time game solver, and a distributed transaction protocol obey different correctness criteria, use different mathematical objects, and address different empirical questions.

2. Tiga as the three-tangle in tripartite entanglement theory

In quantum information, the supplied literature explicitly interprets the query “Tiga” as the three-tangle for the rank-2 family

$$\rho=p\,|GHZ\rangle\langle GHZ|+(1-p)\,|W\rangle\langle W|,\qquad 0\le p\le 1,$$

with

$$|GHZ\rangle=\frac{1}{\sqrt2}\bigl(|000\rangle+|111\rangle\bigr),\qquad |W\rangle=\frac{1}{\sqrt3}\bigl(|001\rangle+|010\rangle+|100\rangle\bigr).$$

These are the two inequivalent canonical classes of genuine three-qubit entanglement, and the paper studies how a tripartite entanglement monotone distinguishes GHZ-type from W-type correlations (Ma et al., 2013).

For pure three-qubit states, the paper uses the Coffman–Kundu–Wootters three-tangle $\tau$, written in CKW form as

$\tau_a=C_{a(bc)}^2-C_{ab}^2-C_{ac}^2,$

with $\tau=\tau_a=\tau_b=\tau_c$ for pure three-qubit states. For mixed states it uses the convex-roof extension

$$\tau(\rho)=\min_{\{p_i,|\psi_i\rangle\}} \sum_i p_i\,\tau(|\psi_i\rangle), \qquad \rho=\sum_i p_i|\psi_i\rangle\langle\psi_i|.$$

The decomposition analysis is built around GHZ/W superpositions

$$|q,\theta\rangle=\sqrt q\,|GHZ\rangle-\sqrt{1-q}\,e^{i\theta}|W\rangle,$$

for which

$$\tau\bigl(|q,\theta\rangle\bigr)=\left| q^2-\frac{8}{9}e^{i3\theta}\sqrt{6q(1-q)^3} \right|.$$

Because the phase enters only through $e^{i3\theta}$, the dependence is periodic with period $2\pi/3$, and the minimum for fixed $$|GHZ\rangle=\frac{1}{\sqrt2}\bigl(|000\rangle+|111\rangle\bigr),\qquad |W\rangle=\frac{1}{\sqrt3}\bigl(|001\rangle+|010\rangle+|100\rangle\bigr).$$0 occurs at $$|GHZ\rangle=\frac{1}{\sqrt2}\bigl(|000\rangle+|111\rangle\bigr),\qquad |W\rangle=\frac{1}{\sqrt3}\bigl(|001\rangle+|010\rangle+|100\rangle\bigr).$$1, so the minimizing phase can be taken as $$|GHZ\rangle=\frac{1}{\sqrt2}\bigl(|000\rangle+|111\rangle\bigr),\qquad |W\rangle=\frac{1}{\sqrt3}\bigl(|001\rangle+|010\rangle+|100\rangle\bigr).$$2.

The exact mixed-state result follows from Carathéodory’s theorem together with this $$|GHZ\rangle=\frac{1}{\sqrt2}\bigl(|000\rangle+|111\rangle\bigr),\qquad |W\rangle=\frac{1}{\sqrt3}\bigl(|001\rangle+|010\rangle+|100\rangle\bigr).$$3-periodicity assumption. Since $$|GHZ\rangle=\frac{1}{\sqrt2}\bigl(|000\rangle+|111\rangle\bigr),\qquad |W\rangle=\frac{1}{\sqrt3}\bigl(|001\rangle+|010\rangle+|100\rangle\bigr).$$4 has rank $$|GHZ\rangle=\frac{1}{\sqrt2}\bigl(|000\rangle+|111\rangle\bigr),\qquad |W\rangle=\frac{1}{\sqrt3}\bigl(|001\rangle+|010\rangle+|100\rangle\bigr).$$5, at most $$|GHZ\rangle=\frac{1}{\sqrt2}\bigl(|000\rangle+|111\rangle\bigr),\qquad |W\rangle=\frac{1}{\sqrt3}\bigl(|001\rangle+|010\rangle+|100\rangle\bigr).$$6 pure states are needed in an optimal convex-roof decomposition. The paper accordingly derives two possible optimal forms: a symmetric 3-state decomposition, and a 4-state decomposition obtained by adjoining either $$|GHZ\rangle=\frac{1}{\sqrt2}\bigl(|000\rangle+|111\rangle\bigr),\qquad |W\rangle=\frac{1}{\sqrt3}\bigl(|001\rangle+|010\rangle+|100\rangle\bigr).$$7 or $$|GHZ\rangle=\frac{1}{\sqrt2}\bigl(|000\rangle+|111\rangle\bigr),\qquad |W\rangle=\frac{1}{\sqrt3}\bigl(|001\rangle+|010\rangle+|100\rangle\bigr).$$8. For the three-tangle, the relevant thresholds are

$$|GHZ\rangle=\frac{1}{\sqrt2}\bigl(|000\rangle+|111\rangle\bigr),\qquad |W\rangle=\frac{1}{\sqrt3}\bigl(|001\rangle+|010\rangle+|100\rangle\bigr).$$9

The qualitative behavior is the central point. The paper shows that:

• $\tau$0 for the entire interval $\tau$1;
• for $\tau$2, the tangle equals the pure-state formula evaluated at $\tau$3;
• for $\tau$4, it becomes a linear function of $\tau$5 and reaches $\tau$6;
• $\tau$7 is a nondecreasing function of $\tau$8.

The same paper compares the three-tangle with three-$\tau$9, defined for pure states by

$\tau_a=C_{a(bc)}^2-C_{ab}^2-C_{ac}^2,$0

with $\tau_a=C_{a(bc)}^2-C_{ab}^2-C_{ac}^2,$1. For the symmetric pure states $\tau_a=C_{a(bc)}^2-C_{ab}^2-C_{ac}^2,$2, one has $\tau_a=C_{a(bc)}^2-C_{ab}^2-C_{ac}^2,$3. The paper derives $\tau_a=C_{a(bc)}^2-C_{ab}^2-C_{ac}^2,$4 for pure three-qubit states and reports that, for the GHZ/W mixture, $\tau_a=C_{a(bc)}^2-C_{ab}^2-C_{ac}^2,$5 persists. The comparison is not merely quantitative: the three-$\tau_a=C_{a(bc)}^2-C_{ab}^2-C_{ac}^2,$6 curve has an interior minimum, whereas the three-tangle is nondecreasing in $\tau_a=C_{a(bc)}^2-C_{ab}^2-C_{ac}^2,$7. This is presented as a sharp example of measure dependence in multipartite entanglement theory (Ma et al., 2013).

3. TIGA-CUB in external pilot-trial methodology

In clinical-trial methodology, TIGA-CUB is a worked example used to redesign an external pilot trial using a formal hypothesis test of feasibility. The trial was a two-arm, parallel-group, individually randomised external pilot trial comparing second-line, short-term, manualised psychoanalytic child psychotherapy versus treatment as usual in children with conduct disorders, with the unit being a child–carer dyad (Wilson et al., 2019).

Its pilot objectives included estimating the consent/recruitment rate among eligible dyads, the amount of missing data in the primary outcome, adherence to the intervention, and parameters needed for the main-study sample size calculation. The original progression criteria required that recruitment was to target, attendance was at more than $\tau_a=C_{a(bc)}^2-C_{ab}^2-C_{ac}^2,$8 of sessions in the intervention arm, and at least $\tau_a=C_{a(bc)}^2-C_{ab}^2-C_{ac}^2,$9 of follow-up data was collected. The pilot used 60 participants total, justified by the familiar rule of thumb of about 30 participants per arm to estimate a common outcome standard deviation.

The methodological contribution of the paper is to replace multiple separate progression criteria with a single feasibility test defined through the power of the planned definitive trial. In the basic setting, the future trial is a two-arm parallel-group trial with a normally distributed primary endpoint, equal randomisation, complete-case intention-to-treat analysis, and initially known outcome variance. If $\tau=\tau_a=\tau_b=\tau_c$0 denotes recruitment, follow-up, and adherence rates, the paper writes definitive-trial power as

$\tau=\tau_a=\tau_b=\tau_c$1

where

$\tau=\tau_a=\tau_b=\tau_c$2

This integrates recruitment, follow-up, and adherence in a single quantitative object rather than treating them conjunctively.

The hypotheses are defined through two thresholds, $\tau=\tau_a=\tau_b=\tau_c$3 and $\tau=\tau_a=\tau_b=\tau_c$4. The null corresponds to definitive-trial power at most $\tau=\tau_a=\tau_b=\tau_c$5, and the alternative corresponds to power at least $\tau=\tau_a=\tau_b=\tau_c$6. The pilot statistic is simply $\tau=\tau_a=\tau_b=\tau_c$7, evaluated at the pilot estimates, with a go/no-go rule of the form $\tau=\tau_a=\tau_b=\tau_c$8.

For the TIGA-CUB redesign, the paper specifies

$\tau=\tau_a=\tau_b=\tau_c$9

and chooses

$$\tau(\rho)=\min_{\{p_i,|\psi_i\rangle\}} \sum_i p_i\,\tau(|\psi_i\rangle), \qquad \rho=\sum_i p_i|\psi_i\rangle\langle\psi_i|.$$0

Under these assumptions, the original pilot size $$\tau(\rho)=\min_{\{p_i,|\psi_i\rangle\}} \sum_i p_i\,\tau(|\psi_i\rangle), \qquad \rho=\sum_i p_i|\psi_i\rangle\langle\psi_i|.$$1 per arm performs poorly: the paper reports that a type I error of about $$\tau(\rho)=\min_{\{p_i,|\psi_i\rangle\}} \sum_i p_i\,\tau(|\psi_i\rangle), \qquad \rho=\sum_i p_i|\psi_i\rangle\langle\psi_i|.$$2 corresponded to a type II error of about $$\tau(\rho)=\min_{\{p_i,|\psi_i\rangle\}} \sum_i p_i\,\tau(|\psi_i\rangle), \qquad \rho=\sum_i p_i|\psi_i\rangle\langle\psi_i|.$$3. By contrast, with $$\tau(\rho)=\min_{\{p_i,|\psi_i\rangle\}} \sum_i p_i\,\tau(|\psi_i\rangle), \qquad \rho=\sum_i p_i|\psi_i\rangle\langle\psi_i|.$$4 per arm, it reports $$\tau(\rho)=\min_{\{p_i,|\psi_i\rangle\}} \sum_i p_i\,\tau(|\psi_i\rangle), \qquad \rho=\sum_i p_i|\psi_i\rangle\langle\psi_i|.$$5 and $$\tau(\rho)=\min_{\{p_i,|\psi_i\rangle\}} \sum_i p_i\,\tau(|\psi_i\rangle), \qquad \rho=\sum_i p_i|\psi_i\rangle\langle\psi_i|.$$6. For the concrete redesign

$$\tau(\rho)=\min_{\{p_i,|\psi_i\rangle\}} \sum_i p_i\,\tau(|\psi_i\rangle), \qquad \rho=\sum_i p_i|\psi_i\rangle\langle\psi_i|.$$7

the rule becomes: go if predicted definitive-trial power exceeds

$$\tau(\rho)=\min_{\{p_i,|\psi_i\rangle\}} \sum_i p_i\,\tau(|\psi_i\rangle), \qquad \rho=\sum_i p_i|\psi_i\rangle\langle\psi_i|.$$8

The paper also compares this framework with conventional independent progression criteria of the form

$$\tau(\rho)=\min_{\{p_i,|\psi_i\rangle\}} \sum_i p_i\,\tau(|\psi_i\rangle), \qquad \rho=\sum_i p_i|\psi_i\rangle\langle\psi_i|.$$9

For the TIGA-CUB example, that conventional strategy is reported to perform extremely poorly: for $$|q,\theta\rangle=\sqrt q\,|GHZ\rangle-\sqrt{1-q}\,e^{i\theta}|W\rangle,$$0, obtaining type I error around $$|q,\theta\rangle=\sqrt q\,|GHZ\rangle-\sqrt{1-q}\,e^{i\theta}|W\rangle,$$1 required accepting type II error around $$|q,\theta\rangle=\sqrt q\,|GHZ\rangle-\sqrt{1-q}\,e^{i\theta}|W\rangle,$$2. The explanation given is structural. Independent progression criteria are conjunctive, whereas feasibility as definitive-trial power is trade-off based: weaker recruitment can be offset by stronger follow-up or adherence, and vice versa. The paper further extends the framework to include pilot estimation of $$|q,\theta\rangle=\sqrt q\,|GHZ\rangle-\sqrt{1-q}\,e^{i\theta}|W\rangle,$$3, reporting that this makes the pilot less efficient and can require still larger sample sizes (Wilson et al., 2019).

4. UPPAAL-TiGA and timed games for worst-case execution time

In real-time verification, UPPAAL-TiGA is used as the engine for solving worst-case execution time as a timed-game optimal reachability problem. The central formal definition is

$$|q,\theta\rangle=\sqrt q\,|GHZ\rangle-\sqrt{1-q}\,e^{i\theta}|W\rangle,$$4

or, with explicit run notation,

$$|q,\theta\rangle=\sqrt q\,|GHZ\rangle-\sqrt{1-q}\,e^{i\theta}|W\rangle,$$5

The reason for the game formulation is that hardware timing is deterministic once the program path and memory references are fixed, whereas the path itself may depend on unknown input data. Those unknown data affect comparisons and branches, so the analysis distinguishes between system-controlled behavior and adversarial input-dependent choices (Cassez, 2010).

The paper assigns Player 1 to the execution of the program on the architecture and Player 2 to the outcomes of comparisons whose operands are unknown. This prevents the conflation of ordinary nondeterminism with data-dependent uncontrollable moves. WCET is then the optimal time for Player 1 to reach the end of the program against all such branch choices.

The methodology has three explicit steps:

1. derive a WCET-equivalent abstract program;
2. compose it with a network of timed automata modeling the architecture;
3. compute WCET as an optimal reachability / winning-time objective.

The abstraction preserves exactly the timing-relevant interface: instruction durations in each pipeline stage, registers read and written, memory cells read and written, and values needed by critical instructions, including status-setting instructions and memory-addressing instructions. The paper formalizes $$|q,\theta\rangle=\sqrt q\,|GHZ\rangle-\sqrt{1-q}\,e^{i\theta}|W\rangle,$$6-equivalence of runs and states that

$$|q,\theta\rangle=\sqrt q\,|GHZ\rangle-\sqrt{1-q}\,e^{i\theta}|W\rangle,$$7

At program level, if $$|q,\theta\rangle=\sqrt q\,|GHZ\rangle-\sqrt{1-q}\,e^{i\theta}|W\rangle,$$8, then

$$|q,\theta\rangle=\sqrt q\,|GHZ\rangle-\sqrt{1-q}\,e^{i\theta}|W\rangle,$$9

The architecture model is a network of timed automata for an ARM9 processor with a 5-stage pipeline—Fetch, Decode, Execute, Memory, Writeback—together with instruction cache, data cache, and main memory. The model includes pipeline stalls, branch prediction with the heuristic “conditional branch is never taken,” flush penalties, FIFO cache replacement, write allocate on write miss, and timing parameters

$$\tau\bigl(|q,\theta\rangle\bigr)=\left| q^2-\frac{8}{9}e^{i3\theta}\sqrt{6q(1-q)^3} \right|.$$0

with one main-memory transaction costing $$\tau\bigl(|q,\theta\rangle\bigr)=\left| q^2-\frac{8}{9}e^{i3\theta}\sqrt{6q(1-q)^3} \right|.$$1 processor cycles.

The TiGA control query used for WCET is given as $2\pi/3$7 If #n is too small, TiGA answers “not controllable”; if it is large enough, TiGA computes the optimal guaranteed reachability time, which the paper reads as the WCET.

The experiments target benchmarks from the Mälardalen WCET benchmark suite on the ARM9 model. The paper reports analyzing 13 out of the 15 programs previously analyzable in METAMOC’s setting. Representative reported results include fac with WCET $$\tau\bigl(|q,\theta\rangle\bigr)=\left| q^2-\frac{8}{9}e^{i3\theta}\sqrt{6q(1-q)^3} \right|.$$2, fib with WCET $$\tau\bigl(|q,\theta\rangle\bigr)=\left| q^2-\frac{8}{9}e^{i3\theta}\sqrt{6q(1-q)^3} \right|.$$3, matmult with WCET $$\tau\bigl(|q,\theta\rangle\bigr)=\left| q^2-\frac{8}{9}e^{i3\theta}\sqrt{6q(1-q)^3} \right|.$$4, and multiple-path programs such as bs, cnt, insertsort, and ns. The comparison emphasized in the paper is with METAMOC + UPPAAL: METAMOC reportedly analyzed only 7 of 15 programs with concrete instruction and data cache, whereas the TiGA-based framework analyzes 13 of 15 under concrete caches, on a 2GHz dual-core laptop with 2GB RAM. The same framework is also extended to dynamic frequency change, with reported low-power opportunities for janne-complex, bs, and fib (Cassez, 2010).

5. Generalizing the Tiga line: TATL verification and symbolic abstractions

A later line of work positions itself directly relative to Uppaal Tiga, treating it as the state-of-the-art tool for two-player timed games with reachability/safety-style objectives and strategy synthesis, and then extending the underlying symbolic methodology to full timed alternating-time temporal logic (TATL) over timed multiplayer games (Jensen et al., 9 Jun 2025).

The paper’s basic distinction is expressiveness. Tiga is organized around a controller-versus-environment view, effectively two-player timed games, whereas the newer formulation handles arbitrary coalitions

$$\tau\bigl(|q,\theta\rangle\bigr)=\left| q^2-\frac{8}{9}e^{i3\theta}\sqrt{6q(1-q)^3} \right|.$$5

allows nesting of coalition modalities, and supports the freeze operator

$$\tau\bigl(|q,\theta\rangle\bigr)=\left| q^2-\frac{8}{9}e^{i3\theta}\sqrt{6q(1-q)^3} \right|.$$6

Bounded until is then derived as

$$\tau\bigl(|q,\theta\rangle\bigr)=\left| q^2-\frac{8}{9}e^{i3\theta}\sqrt{6q(1-q)^3} \right|.$$7

The paper makes the overlap explicit: of 236 total queries, 150 have no nested coalitions and can also be solved by Uppaal Tiga. This is the operational content of the statement that Tiga can verify only a strict subset of TATL.

Algorithmically, the work uses the extended abstract dependency graph (EADG) framework. Vertices are symbolic proof obligations of the form $$\tau\bigl(|q,\theta\rangle\bigr)=\left| q^2-\frac{8}{9}e^{i3\theta}\sqrt{6q(1-q)^3} \right|.$$8, where $$\tau\bigl(|q,\theta\rangle\bigr)=\left| q^2-\frac{8}{9}e^{i3\theta}\sqrt{6q(1-q)^3} \right|.$$9 is a symbolic state and $e^{i3\theta}$0 is a TATL subformula. The symbolic heart of the method is a pair of coalition predecessor operators,

$e^{i3\theta}$1

which generalize Tiga-style timed-game predecessors to existential and universal coalition until modalities.

One major contribution is a generalized form of inclusion checking expressed as vertex merging in the EADG setting. In the concrete TATL encoding, if

$e^{i3\theta}$2

then the smaller symbolic obligation is derivable from the larger one via

$e^{i3\theta}$3

This is the formal restatement of classical inclusion checking.

A second, practically stronger contribution is the expansion abstraction

$e^{i3\theta}$4

Instead of dynamically testing whether a newly generated zone is included in an older one, the method eagerly lifts every generated vertex to the maximal zone permitted by the location invariant. The result is effectively one vertex per location-formula pair rather than per location-zone-formula triple. The paper proves that this abstraction preserves correctness for the satisfaction question at the root states of interest.

The experimental conclusions are stated quantitatively. The abstract reports that the new abstraction yields almost two orders of magnitude faster performance than the naive method. On the overlapping fragment, the paper reports that Incl+Unsat and Tiga+Unsat have similar performance on challenging queries, while a modified Tiga+Expand+Unsat matches the new method and is almost an order of magnitude faster than the previous state-of-the-art Tiga implementation. Thus, in this line of work, Tiga is both a baseline and a beneficiary: the paper extends beyond Tiga’s traditional expressiveness while also improving Tiga itself (Jensen et al., 9 Jun 2025).

6. Tiga as a geo-distributed transaction protocol

In distributed systems, Tiga names a geo-replicated transaction protocol designed to make strictly serializable transactions commit in 1 wide-area round-trip time (1 WRTT) in common cases while preserving fault-tolerant replication, scalability across shards, and high throughput with low CPU overhead (Geng et al., 6 Sep 2025).

The protocol’s architectural move is to stop treating concurrency control and consensus as separate ordering problems. Instead, it consolidates them into one protocol round and uses synchronized clocks to proactively assign each transaction a future timestamp at submission time. If a transaction reaches the relevant servers before that timestamp, then all servers can process it in the same timestamp order, so serialization and replication decisions align in one WAN round. If proactive ordering fails because the transaction is delayed, the protocol falls back to a slow path committing in 1.5–2 WRTTs.

The timestamp initialization is

$e^{i3\theta}$5

where $e^{i3\theta}$6 is a super quorum of the closest replicas in shard $e^{i3\theta}$7, and the implementation uses

$e^{i3\theta}$8

The transaction is multicast to all replicas of all participating shards. Each server maintains a timestamp-ordered priority queue pq, an ordered log, sync-point, commit-point, and per-key timestamp maps rMap and wMap for conflict detection.

A transaction is not accepted if a server has already released a conflicting transaction with a larger timestamp. If conflict detection fails, a leader may update the timestamp to its current local clock time and insert the transaction, whereas a follower waits for leader synchronization in the slow path. Servers wait until local time passes the timestamp and no conflicting earlier-timestamp transaction remains ahead in the queue. Followers then send fast replies without executing the transaction. Leaders optimistically execute, send fast replies containing transaction id, timestamp, state hash, and execution result, and then perform timestamp agreement with the other participating leaders.

A shard is fast-committed if the coordinator receives a super quorum of fast replies from that shard, all with the same hash and timestamp, and the set includes the leader. The super quorum size is

$e^{i3\theta}$9

Across shards, leaders compute

$2\pi/3$0

The protocol distinguishes three timestamp-agreement cases: all leaders already agree; one leader already used the maximum timestamp while others did not; or a leader used a smaller timestamp and must revoke, update, reposition, and later re-execute. To support this, Tiga maintains multiple versions of data items so that invalid speculative versions can be erased internally.

The correctness claims are per-shard linearizability and strict serializability across shards. A central issue is timestamp inversion, where real-time order can contradict serial order if different shards release transactions without enough cross-shard coordination. The protocol’s fix is the second round of timestamp agreement in the relevant cases. The discussion is explicit that correctness does not depend on bounded clock error; clocks are used for performance, not correctness.

The evaluation compares Tiga against 2PL+Paxos, OCC+Paxos, Tapir, Janus, Calvin+, Detock, and NCC/NCC+. It reports 1.3–7.2× higher throughput and 1.4–4.6× lower latency than the compared baselines. In MicroBench at low contention, the maximum throughput numbers reported are $2\pi/3$1K txns/s for 2PL+Paxos, $2\pi/3$2K for Tapir, $2\pi/3$3K for Janus, $2\pi/3$4K for Calvin+, and 157.3K for Tiga. In TPC-C, the reported maximum throughput rises to 21.6K for Tiga, compared with $2\pi/3$5K for Janus and $2\pi/3$6K for Detock. The paper further reports that when leaders are separated across regions, Tiga throughput drops by 9.7% to 141.9K txns/s, and that in a MicroBench run at 80K txns/s, killing one shard leader yields global view change and recovery in 3.8 seconds (Geng et al., 6 Sep 2025).

7. Cross-domain significance and limits of the name

Across these uses, “Tiga” has no stable cross-disciplinary technical definition. In one setting it is a shorthand reading of the three-tangle; in another it is embedded in TIGA-CUB as a trial name; in formal verification it denotes UPPAAL-TiGA and a broader algorithmic lineage of timed-game solving; in distributed systems it is the proper name of a 1-WRTT transaction protocol (Ma et al., 2013, Wilson et al., 2019, Cassez, 2010, Jensen et al., 9 Jun 2025, Geng et al., 6 Sep 2025).

This suggests that the term functions primarily as a local identifier rather than a portable concept. The technically important object is therefore not the word itself but the formal structure attached to it in each domain: a convex-roof entanglement monotone, a feasibility-testing framework for pilot trials, a timed-game controller-synthesis engine, an EADG-based TATL model checker, or a timestamp-driven geo-transaction protocol.

A common misconception would be to treat these uses as variants of a single framework. The supplied literature does not support that reading. The only direct lineage appears within timed verification, where the TATL work is explicitly positioned as extending and accelerating Uppaal Tiga. Elsewhere, the name is merely reused. Accordingly, precise interpretation requires immediate attention to domain, notation, and citation context.