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arxiv: 2603.11684 · v2 · submitted 2026-03-12 · 🧬 q-bio.MN

DNA Ternary Full Adder

Enqiang Zhu , Peize Qiu , Xianhang Luo , Chanjuan Liu , Jin Xu This is my paper

Pith reviewed 2026-05-15 12:08 UTC · model grok-4.3

classification 🧬 q-bio.MN
keywords DNA computingternary logicfull addercompetitive blockingmolecular circuitsmulti-valued logicbiochemical computation
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The pith

A DNA competitive blocking circuit recognizes all ternary input triples and produces correct outputs for 17-trit addition.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that a DNA-based competitive blocking circuit can distinguish and compute every possible combination of three ternary digits for a full adder. Paired with a dynamic concentration adjustment step, the design raises the number of trits that can be handled in a single biochemical run. Experiments confirm the circuit returns the expected sum and carry digits across the tested cases, reaching 17-trit ternary addition. This provides the first working DNA implementation of ternary addition and addresses the larger input space that ternary logic requires compared with binary.

Core claim

A novel ternary full adder architecture uses a competitive blocking circuit to recognize and compute all three-input ternary combinations, combined with a dynamic concentration adjustment strategy; biochemical experiments confirm that the circuit produces correct output digits and achieves 17-trit ternary addition.

What carries the argument

The competitive blocking (CB) circuit, which distinguishes every three-input ternary combination and blocks unwanted reactions to yield the correct sum and carry.

If this is right

  • The CB circuit yields the correct output digits for a ternary full adder.
  • The approach achieves 17-trit ternary addition in biochemical experiments.
  • The CA strategy increases the number of trits that can be processed.
  • The design supplies a methodological foundation for DNA-based ternary logic circuits.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the circuit scales without cumulative error, larger trit lengths become feasible by repeating the CA step.
  • The same recognition mechanism could be reused to build other ternary arithmetic blocks such as multipliers.
  • Integration with existing DNA strand-displacement gates might allow mixed binary-ternary molecular processors.

Load-bearing premise

The competitive blocking circuit can accurately recognize and compute every three-input ternary combination without interference or errors across the full input range in a biochemical setting.

What would settle it

A single biochemical run in which the circuit produces an incorrect sum or carry digit for any tested ternary input triple, such as inputs 0-1-2.

Figures

Figures reproduced from arXiv: 2603.11684 by Chanjuan Liu, Enqiang Zhu, Jin Xu, Peize Qiu, Xianhang Luo.

Figure 1
Figure 1. Figure 1: The illustration depicts the operational mechanism of the CB circuit, which encompasses three core reactions corresponding to Equations 1, 2, and 3. All reactions involving GATE1i j are represented by gray arrows, while those involving GATE2 are indicated with red arrows. It is particularly noteworthy that the reaction efficiency between GATE1i j and Bin is the highest. To emphasize this significant differ… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Test schemes for different toehold lengths in the GATE1i j structure. (b) Polyacrylamide gel electrophoresis (PAGE) results show binding between Bin and GATE1i j in the CB circuit at different concentration ratios, where the relative concentration of each band is determined by its brightness. (c) Fluorescence detection results for SUM1 product generated by the CB circuit when the toehold lengths of GAT… view at source ↗
Figure 3
Figure 3. Figure 3: (a) Truth table for the ternary adder. (b) Modular processing of the ternary adder based on its truth table. (c) Fluorescence curves for all reactions of the half adder. The results were normalized to the maximum fluorescence across all samples, and a fluorescence reading above 0.5 was considered a valid output. (d) Fluorescence curves for the SUM2 result in the 1-trit full adder. The current results were … view at source ↗
Figure 4
Figure 4. Figure 4: Generation and processing of carry information strands. (a) Schematic diagram of the three-input AND gate reaction for processing the first type of scenarios. (b) Schematic diagram of the two-input AND gate reaction for processing the second type of scenarios. (c) Extraction operation for the carry information strands. Cout. We employed the i j-module to compute the addition of two addend inputs alongside … view at source ↗
Figure 5
Figure 5. Figure 5: (a) Schematic diagram of the catalytic reaction for the carry information strand. (b) Reaction network of a multi-trit full adder calculating 1012122101 + 2210221122. (c) The sum of two ten-digit ternary numbers. The final sum is read from the high digit to the low digit. (d) Computational performance of the ternary adder under continuous-carry conditions without the CA strategy, illustrated with the examp… view at source ↗
read the original abstract

As transistor dimensions continue to shrink, binary devices are rapidly approaching their fundamental limits in power density. In response, multi-valued systems have attracted significant attention due to their enhanced information density. Among these, the ternary system stands out as the most practical option, being the closest integer base to (e), which is considered optimal for information efficiency. Despite the intrinsic advantages of DNA nanomaterials, such as programmability, energy efficiency, and massive parallelism, their application in ternary logic remains largely unexplored, particularly in the realm of ternary addition circuits. This gap can be attributed to a fundamental challenge: ternary logic requires circuits capable of recognizing and processing a far larger set of input combinations than binary systems, a task that existing models and techniques often struggle to accomplish. In this work, we propose a novel architecture for a ternary full adder. Our design includes a competitive blocking (CB) circuit that enables the recognition and computation of all possible three-input ternary combinations. Coupled with a dynamic concentration adjustment (CA) strategy, this approach significantly enhances the number of trits that can be processed. Biochemical experiments demonstrate that the CB circuit successfully yields the correct output digits for a ternary full adder, achieving 17-trit ternary addition. To our knowledge, this work represents the first successful DNA-based ternary adder, establishing a new methodological foundation for DNA computing and highlighting its considerable potential for scalable digital information processing.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a competitive blocking (CB) circuit to recognize and compute all 27 three-input ternary combinations, paired with a dynamic concentration adjustment (CA) strategy, to realize a DNA-based ternary full adder. Biochemical experiments are reported to confirm that the circuit produces correct output digits, enabling 17-trit ternary addition and constituting the first such DNA ternary adder.

Significance. If the experimental results are robust, this establishes a practical foundation for ternary logic in DNA computing, leveraging DNA programmability to achieve higher information density than binary systems while addressing the challenge of handling expanded input sets. The reported scaling to 17 trits via the CB+CA approach would represent a concrete advance in scalable molecular computation.

major comments (2)
  1. [Results] Results section (biochemical experiments): The central claim that the CB circuit yields correct outputs for 17-trit addition rests on the reported experiments, yet the manuscript provides insufficient quantitative data on error rates, controls for all 27 input combinations, sequence designs, and raw fluorescence/gel measurements. This weakens support for the scalability assertion and the assumption that the circuit operates without interference across the full input range.
  2. [Methods] Methods (CA strategy implementation): The dynamic concentration adjustment strategy is described at a high level but lacks explicit protocols for how concentrations are tuned in the biochemical setting to prevent crosstalk or incomplete reactions when scaling beyond small numbers of trits.
minor comments (2)
  1. [Abstract] Abstract: The phrase 'achieving 17-trit ternary addition' should clarify whether this refers to a single 17-trit number or multi-trit operations with carry propagation.
  2. [Introduction] Introduction: The claim that ternary is 'the most practical option' closest to e would benefit from a brief citation to information-theoretic results on optimal radix.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which will help improve the clarity and robustness of our presentation. We address each major comment below and will incorporate the requested details in the revised manuscript.

read point-by-point responses

  1. Referee: [Results] Results section (biochemical experiments): The central claim that the CB circuit yields correct outputs for 17-trit addition rests on the reported experiments, yet the manuscript provides insufficient quantitative data on error rates, controls for all 27 input combinations, sequence designs, and raw fluorescence/gel measurements. This weakens support for the scalability assertion and the assumption that the circuit operates without interference across the full input range.

    Authors: We agree that additional quantitative details will strengthen the support for our claims. In the revised manuscript, we will add error rates derived from replicate experiments, explicit controls confirming correct outputs across all 27 input combinations, complete sequence designs placed in the supplementary information, and the raw fluorescence and gel measurements. These expansions will directly demonstrate the absence of significant interference and better justify the observed scalability to 17 trits. revision: yes

  2. Referee: [Methods] Methods (CA strategy implementation): The dynamic concentration adjustment strategy is described at a high level but lacks explicit protocols for how concentrations are tuned in the biochemical setting to prevent crosstalk or incomplete reactions when scaling beyond small numbers of trits.

    Authors: We will expand the Methods section to provide explicit protocols for the CA strategy. The revised text will specify the concentration values used at each scale, the timing and criteria for dynamic adjustments, and the biochemical measures employed to avoid crosstalk and incomplete reactions, including sequence orthogonality verification and buffer optimization. revision: yes

Circularity Check

0 steps flagged

No circularity; experimental demonstration stands on reported biochemical results

full rationale

The paper presents a DNA-based ternary full adder implemented via competitive blocking (CB) circuits plus concentration adjustment (CA). Its core claim is that biochemical experiments confirm correct output for all 27 input combinations and scale to 17 trits. No derivation chain, first-principles prediction, or fitted-parameter step exists; the manuscript reports direct experimental outcomes (fluorescence/gel data and controls) rather than any mathematical reduction that could collapse to its own inputs. Self-citations, if present, are not load-bearing for the headline result. The work is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

The central claim rests on standard domain assumptions from DNA computing about reliable strand interactions and the effectiveness of the newly introduced circuit designs; no free parameters or new physical entities are introduced.

axioms (1)
  • domain assumption DNA strand displacement and hybridization reactions can be programmed to implement reliable logic operations without significant crosstalk.
    Invoked to support the function of the competitive blocking circuit for all ternary input combinations.
invented entities (2)
  • Competitive Blocking (CB) circuit no independent evidence
    purpose: To recognize and compute all possible three-input ternary combinations.
    Newly proposed DNA circuit architecture; independent evidence limited to the reported experiments.
  • Dynamic concentration adjustment (CA) strategy no independent evidence
    purpose: To enhance the number of trits that can be processed.
    Newly proposed strategy to improve scalability of the adder; no external validation cited.

pith-pipeline@v0.9.0 · 5547 in / 1402 out tokens · 46126 ms · 2026-05-15T12:08:51.537769+00:00 · methodology

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