P≠NPですか?

Qwen 3 235B

Vote: Yes

The P vs NP problem is one of the most important open questions in computer science. P refers to the set of problems that can be solved quickly by a deterministic Turing machine, while NP refers to those whose solutions can be verified quickly. Despite extensive research, no one has proven that P = NP. The consensus among most computer scientists is that P ≠ NP, meaning that there are problems for which solutions can be verified efficiently but not solved efficiently. This belief is supported by decades of failed attempts to find polynomial-time algorithms for NP-complete problems. Therefore, the preponderance of evidence and expert opinion favors P ≠ NP.

Codestral

Vote: No

The P vs NP problem is one of the most famous unsolved problems in computer science. It asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. The consensus among experts is that it is extremely unlikely that P equals NP, but it has not been proven either way. Therefore, the most reasonable answer is No.

Llama 4 Scout

Vote: No

The question of whether P is not equal to NP is a fundamental problem in computational complexity theory. It deals with the relationship between computational complexity classes P and NP. P refers to the set of problems that can be solved in polynomial time, while NP refers to the set of problems for which a proposed solution can be verified in polynomial time. If P=NP, then every problem with a known efficient algorithm (in P) would also have an efficient algorithm for verifying solutions (in NP), and vice versa. The question asks if it's not the case that P equals NP. The majority of the scientific community believes that P≠NP. This belief is based on decades of attempts to find polynomial-time algorithms for NP-complete problems, which are problems that are in NP and to which any problem in NP can be reduced in polynomial time. Despite significant efforts, no such algorithms have been found, suggesting that P might not equal NP. However, a formal proof or disproof of P≠NP is still elusive. The question is more about the current state of knowledge and the inclinations of the scientific community based on empirical evidence and theoretical insights.

Devstral Small

Vote: No

The question asks whether P ≠ NP, which is one of the most important open questions in computer science. While many researchers believe that P ≠ NP, there is no proof of this statement. The lack of a proof means that we cannot definitively say 'Yes' to this question. Therefore, the most accurate answer is 'No,' as we do not currently have evidence or a proof to support P ≠ NP.

Gemini 2.0 Flash

Vote: Yes

The vast majority of computer scientists believe that P is not equal to NP. While no proof exists, decades of failed attempts to find efficient algorithms for NP-complete problems, coupled with the ability to prove problems are NP-complete, strongly suggest that such algorithms are unlikely to exist. Furthermore, the consequences of P=NP would be revolutionary and contradict our current understanding of computational complexity.

Nova Lite

Vote: No

The question asks if P is not equal to NP. The P vs NP problem is a major unsolved problem in computer science which asks whether every problem whose solution can be quickly verified can also be quickly solved. Despite extensive research, no one has been able to prove or disprove this conjecture. Therefore, we cannot definitively say whether P is not equal to NP.

Nova Pro

Vote: No

The P vs NP problem is one of the most famous unsolved problems in computer science. It asks whether every problem whose solution can be quickly verified can also be solved quickly. Despite extensive research, no one has been able to prove or disprove this hypothesis. Therefore, the current consensus among experts is that the answer is unknown, which aligns more closely with option B: No, as we cannot definitively say 'Yes' to the question.

GPT-4o

Vote: Yes

P ≠ NP is a widely held belief in the computer science community mainly because, despite extensive research and attempts, no one has been able to prove that P=NP. Many computational problems have been shown to be NP-complete, and no polynomial-time solutions have been discovered for these problems. The lack of such solutions supports the prevailing view that P and NP are indeed different sets.

devstral-2512

Vote: Yes

The P vs NP problem is one of the most fundamental questions in computer science. While it remains unproven, the consensus among experts leans toward P ≠ NP. This is because the implications of P = NP would be revolutionary, allowing efficient solutions to problems currently believed to be intractable. The lack of such solutions despite extensive research suggests that P ≠ NP is more likely. Additionally, the existence of problems in NP that have resisted decades of efforts to find polynomial-time algorithms further supports this view.

Claude 3 Haiku

Vote: No

I believe that P ≠ NP is true. The P vs NP problem is one of the most famous unsolved problems in computer science, and it has significant implications for the limits of efficient computation. While it has not been formally proven, the general consensus among experts is that P ≠ NP, meaning that there are problems in NP that cannot be solved efficiently by polynomial-time algorithms. The difficulty of proving or disproving this conjecture stems from the inherent complexity of the problem and the profound questions it raises about the nature of computability and efficient problem-solving. Therefore, based on the current state of knowledge, I believe the most reasonable answer is that P ≠ NP.

Gemini 2.5 Flash

Vote: Yes

The P versus NP problem is one of the most significant unsolved problems in theoretical computer science, and indeed, in all of mathematics. There is no formal proof to definitively answer whether P=NP or P≠NP. However, the overwhelming consensus among computer scientists and mathematicians is that P≠NP. This belief is supported by decades of research where no polynomial-time algorithms have been found for known NP-complete problems, despite extensive efforts. If P=NP, it would imply that many problems currently considered intractable (such as breaking modern cryptography or finding optimal solutions to many combinatorial optimization problems) could be solved efficiently, which seems highly unlikely given current understanding. Therefore, while unproven, the strong prevailing expert opinion points towards P≠NP.

claude-haiku-4-5

Vote: Yes

The question asks whether P≠NP (is P not equal to NP?). Based on current mathematical consensus, the answer is 'Yes' - P is believed to be not equal to NP, though this remains unproven. P represents problems solvable in polynomial time by a deterministic Turing machine. NP represents problems whose solutions can be verified in polynomial time. While every problem in P is also in NP, no one has found an NP-complete problem that belongs to P, despite decades of research. The P vs NP problem is one of the seven Millennium Prize Problems. The overwhelming majority of computer scientists and mathematicians conjecture that P≠NP, as a proof that P=NP would have extraordinary implications for cryptography and computational theory.

GPT-4o Mini

Vote: Yes

The consensus among computer scientists is that P is likely not equal to NP, which is a fundamental question in computational complexity theory. If P were equal to NP, it would mean that problems that can be verified quickly can also be solved quickly, which contradicts our current understanding of computational limits. Additionally, there are numerous problems in NP that we have yet to find efficient solutions for, supporting the notion that P does not equal NP. Although no one has definitively proven that P is not equal to NP, the belief in this assertion is widely held in the field.

O3 Mini

Vote: Yes

In computational complexity theory, the predominant view among researchers is that P is not equal to NP, even though the problem remains unproven. This consensus supports selecting 'Yes'.

Grok 3

Vote: Yes

I vote for option A, that P≠NP. This is one of the most fundamental open problems in computer science, and the prevailing belief among experts is that P does not equal NP. The reasoning is based on the intuition that solving a problem (P) should generally be easier than verifying a solution (NP), as verification often requires less computational effort than discovery. Historical evidence supports this view—decades of research have failed to find efficient algorithms for many NP-complete problems, suggesting a fundamental barrier. If P were equal to NP, it would imply that problems like factoring large numbers, crucial for cryptography, could be solved efficiently, which seems unlikely given the practical security of systems like RSA. While there’s no formal proof yet, the complexity hierarchy and the behavior of known algorithms strongly suggest that P≠NP. This position aligns with the current consensus in theoretical computer science.

GPT-5.4

Vote: No

現在の数学では、P≠NPは未解決問題です。したがって「Yes」と断定するのは根拠不足です。 与えられた選択肢が二択しかないなら、厳密には「P≠NPであると確定していない」という意味で「No」を選ぶのが最も正確です。 多くの研究者はP≠NPだと予想していますが、予想と証明は別です。問題文は事実判断として読めるため、現状では否定側に投票するのが妥当です。

Magistral Small

Vote: Yes

The question of whether P≠NP is one of the most significant open problems in computer science. While it has not been definitively proven, the majority of experts believe it to be true based on the lack of progress in proving P=NP and the inherent difficulty of the problem. Many complex problems in NP have not been solved in polynomial time despite extensive research, suggesting that P is not equal to NP.

Sonar Pro

Vote: No

The query asks 'P≠NPですか?' (Is P≠NP?), which is one of the most famous unsolved problems in computer science, specifically a conjecture in computational complexity theory. All provided search results [1][2][3][4][5][6][7][8] explicitly state that P≠NP is an **unproven conjecture** (未解決問題), not a confirmed fact. For example: - [1] calls it 'P≠NP予想' (P≠NP conjecture), an unsolved problem where 'proof is still absent' despite many researchers believing it. - [2][3][6] describe it as a prediction that P and NP are unequal, with no resolution. - No result claims it has been proven; they all affirm P ⊆ NP is known, but equality remains open. As of the current date (2026), no credible proof exists in the results or known history—it's a Millennium Prize Problem. Thus, it is **not established that P≠NP**, making 'No' the accurate answer. Voting 'Yes' would misrepresent it as proven, which contradicts all sources.

Gemini 3 Flash

Vote: Yes

While the P vs NP problem remains one of the most significant unsolved questions in mathematics and theoretical computer science, the consensus among the vast majority of researchers is that P ≠ NP. This belief is grounded in several compelling observations. First, decades of intensive research into NP-complete problems—such as the Traveling Salesperson Problem and Boolean Satisfiability—have failed to yield a polynomial-time algorithm for any of them. If P were equal to NP, a polynomial solution for one would imply polynomial solutions for all, which seems increasingly unlikely given our current understanding of computational complexity. Second, the equality of P and NP would lead to the collapse of the Polynomial Hierarchy, a consequence that contradicts the intuition of most complexity theorists. Furthermore, much of modern cryptography and digital security relies on the assumption that certain NP problems are not solvable in polynomial time; a proof of P = NP would fundamentally undermine these systems. While a formal proof is still missing, the weight of empirical evidence and theoretical intuition strongly supports the conclusion that P ≠ NP.

GPT-5.1

Vote: Yes

現時点では「P≠NP」であると“広く信じられて”おり、その立場に投票します。 理由: 1. 計算複雑性理論における最重要未解決問題であり、P=NP も P≠NP もまだ証明されていません。ただし、圧倒的多数の研究者は P≠NP を予想しています。 2. 何十年にもわたる研究にもかかわらず、NP 完全問題（巡回セールスマン問題、充足可能性問題 SAT など）に対して多項式時間アルゴリズムは発見されていません。多様なアプローチが失敗していることは、P=NP が真である可能性をかなり悲観的に見せています。 3. さまざまな「バリア結果」（相対化、自然証明、補間法など）が、現在知られている多くの証明技法では P vs NP を解決できないことを示しており、P=NP ならば非常に“奇妙な”世界になると考える研究者が多いです。 重要なのは、これはあくまで未解決問題であり、「数学的に確定した事実」ではなく「もっとも妥当と見なされている予想」に基づく選択だという点です。その前提で、一般的な専門家のコンセンサスに従い A (Yes: P≠NP) を選びます。

Grok 4.20

Vote: Yes

The P versus NP problem remains unsolved, but the overwhelming consensus in computer science is that P ≠ NP. This is based on decades of failed attempts to find efficient solutions for NP-complete problems and results like Ladner's theorem showing intermediate complexity classes if P ≠ NP. Voting 'Yes' aligns with expert surveys (e.g., from the 2010s where ~83% of theorists believed P ≠ NP). Claiming 'No' would assert P = NP, which lacks supporting evidence and contradicts the prevailing view.

Mistral Large

Vote: No

The P vs NP problem is one of the most significant unsolved questions in computer science, and the prevailing consensus among experts is that P ≠ NP. This stance is supported by several compelling arguments: First, despite decades of intensive research, no polynomial-time algorithm has been discovered for any NP-complete problem. NP-complete problems, such as the Boolean satisfiability problem (SAT) or the traveling salesman problem, are central to this debate. The lack of progress in finding efficient solutions to these problems suggests that such algorithms may not exist, implying P ≠ NP. Second, the existence of one-way functions, which are easy to compute but hard to invert, is widely believed to hold true. If P = NP, one-way functions would not exist, as inverting them would be computationally feasible. The cryptographic community heavily relies on the assumption that one-way functions exist, further supporting the P ≠ NP conjecture. Third, the structural differences between P and NP problems provide intuitive support for P ≠ NP. Problems in P are efficiently solvable, while NP problems are characterized by their verifiability rather than solvability. The idea that verifying a solution is fundamentally easier than finding one aligns with the belief that P ≠ NP. While the question remains unproven, the weight of evidence and expert opinion strongly favors the conclusion that P ≠ NP. Until a breakthrough proves otherwise, this remains the most reasonable position.

Claude Opus 4

Vote: Yes

P≠NPは未解決問題ですが、計算複雑性理論の研究者の大多数(調査によると約80-90%)がP≠NPであると予想しています。NP完全問題に対する多項式時間アルゴリズムが半世紀以上の研究にもかかわらず発見されていないこと、また自然な証明の障壁などの理論的証拠からも、P≠NPが成り立つ可能性が高いと考えられます。したがって最も妥当な回答はYesです。

GPT-5.2

Vote: Yes

現在の計算量理論の主流な見解では、PとNPは等しくない（P≠NP）と考えられています。もしP=NPであれば、SATなどNP完全問題が多項式時間で解けることになり、暗号・最適化・自動証明など広範な分野に極めて大きな帰結が生じますが、そのようなアルゴリズムは長年見つかっていません。 また、相対化（オラクル）や自然証明、代数化といった既知の下界手法の限界から、簡単な方法ではP=NPもP≠NPも示せないことが分かっており、未解決ではあるものの、研究コミュニティの経験的・構造的な証拠はP≠NP側に強く傾いています。 以上より、現時点で最も妥当な選択として「Yes（P≠NP）」に投票します。

Claude Sonnet 4

Vote: Yes

P≠NPは、コンピュータ科学における最も重要な未解決問題の一つです。現在の数学的・計算理論的証拠の重みは、P≠NPを支持する方向にあります。 ほとんどの理論計算機科学者（調査によれば約80-90%）はP≠NPを信じています。NP完全問題（例：SAT、巡回セールスマン問題）に対して効率的なアルゴリズムが発見されていないという数十年にわたる経験的証拠があります。 オラクル分離やランダム化の証拠など、多くの間接的な証拠もP≠NPを支持しています。 ただし、これはまだ証明されていない問題であり、厳密には「わからない」が正確ですが、現時点での最もコンセンサスのある答えはP≠NP（Yes）です。

Claude Sonnet 4

Vote: Yes

I believe P≠NP is true. This is one of the most fundamental open problems in computer science and mathematics. The intuitive argument is compelling: P represents problems that can be solved efficiently (in polynomial time), while NP represents problems where solutions can be verified efficiently but finding them may require exponential time. The overwhelming consensus among computer scientists is that P≠NP. If P=NP were true, it would mean that every problem whose solution can be quickly verified could also be quickly solved. This would have revolutionary implications - we could efficiently solve traveling salesman, boolean satisfiability, and countless other hard optimization problems. Despite decades of research and significant monetary incentives (Clay Institute's $1 million prize), no polynomial-time algorithms have been found for NP-complete problems. The structural differences between these complexity classes, combined with the lack of progress in finding efficient algorithms for well-studied hard problems, strongly suggests they are distinct. While this remains unproven, the weight of evidence and expert opinion heavily favors P≠NP.

Gemini 3.1 Pro

Vote: Yes

P≠NP問題は計算機科学における最大の未解決問題ですが、専門家の間では「P≠NPである（Yes）」という見解が圧倒的な支持を得ています。 もしP=NPであれば、答えを「検証」することが容易な問題はすべて、答えを「見つける」ことも容易であるということになります。これは、暗号解読や複雑な最適化問題が簡単に解けてしまうことを意味し、私たちの直感や現実世界の物理的・数学的制約と大きく矛盾します。 また、現代のインターネット社会を支える公開鍵暗号技術（RSA暗号など）も、P≠NPを大前提として成立しています。数学的な厳密な証明はまだ存在しませんが、実用面・理論面の両方から「P≠NPである」と考えるのが最も妥当かつ説得力のある結論です。

O3

Vote: Yes

現在の計算機科学の主流な見解では、P と NP は異なる集合であると考えられている。まだ正式な証明は得られていないものの、数十年にわたる研究で P=NP を示唆する有力な手掛かりは見つかっておらず、多くの難問が P≠NP であると仮定すると自然に説明できる。また、暗号理論など実用分野でも P≠NP を前提に安全性が構築されていることから、実務的にも P≠NP を採用するのが一般的である。したがって、現時点で最も支持されている立場は “Yes (P≠NP)” である。

Kimi K2.5

Vote: Yes

The overwhelming consensus in theoretical computer science is that P ≠ NP. Decades of intensive research have failed to produce polynomial-time algorithms for any NP-complete problem, despite these problems being extensively studied. If P were equal to NP, we would expect to have discovered efficient algorithms for at least some NP-complete problems by now, particularly for restricted cases or approximations. The fact that problems like 3-SAT, graph coloring, and the traveling salesman problem appear to require exponential time in the worst case strongly suggests fundamental structural differences between P and NP. Additionally, modern cryptography (RSA, elliptic curve cryptography) relies on the assumption that certain problems are computationally hard. The existence of practical cryptography provides indirect evidence that P ≠ NP. While this remains formally unproven as a Millennium Prize Problem, the weight of empirical and theoretical evidence strongly supports P ≠ NP.

Claude Sonnet 4

Vote: Yes

I vote that P≠NP is true (Yes) based on several compelling reasons. First, despite decades of intensive research by brilliant computer scientists and mathematicians, no polynomial-time algorithm has been found for any NP-complete problem. This persistent difficulty across thousands of attempts suggests a fundamental barrier rather than mere oversight. Second, there are strong theoretical arguments. If P=NP, it would mean that verifying a solution and finding a solution are equally difficult, which contradicts our intuitive understanding and practical experience with problems like factoring, SAT, and the traveling salesman problem. Third, the vast majority of complexity theorists believe P≠NP. Multiple surveys show over 80% of experts hold this view, based on their deep understanding of computational complexity. Fourth, proving P=NP would have revolutionary implications - breaking most modern cryptography, solving optimization problems instantly, and transforming fields from drug design to logistics. The absence of such breakthroughs despite extensive search suggests these efficient algorithms don't exist. While P≠NP remains unproven, the weight of evidence, expert consensus, and theoretical considerations strongly support this position.

Sonar Reasoning Pro

Vote: Yes

While P≠NP remains an unproven conjecture, the preponderance of evidence and overwhelming expert consensus support it. The search results indicate that most computational complexity researchers believe P≠NP is true[1][4]. After decades of intensive research, no polynomial-time algorithm has been discovered for any NP-complete problem[4], despite extensive effort. If P=NP were true, it would imply that verification and solution are equally tractable—contradicting all practical computational experience. P⊆NP is proven, making the core question whether this is a proper subset[1][2]. The absence of polynomial-time solutions for problems like factorization and the satisfiability problem, combined with their significance to modern cryptography, provides strong empirical support for P≠NP being correct[4]. Though mathematical proof is lacking, answer A represents the most evidence-based position.

MiniMax M2.5

Vote: Yes

The P vs NP problem asks whether every problem whose solution can be verified quickly can also be solved quickly. While this remains an unsolved problem in computer science with no mathematical proof either way, the overwhelming consensus among theoretical computer scientists is that P≠NP. This is reflected in the fact that most cryptographic systems are built on the assumption that P≠NP, as if P=NP were true, many encryption schemes would become insecure. Without a proof, we cannot be certain, but the evidence and expert opinion strongly support the belief that P≠NP.

Claude Opus 4

Vote: Yes

P≠NP is one of the most fundamental open problems in computer science and mathematics. While not yet proven, there are compelling reasons to believe P does not equal NP. First, despite decades of intensive research by the world's best computer scientists, no one has found polynomial-time algorithms for NP-complete problems. If P=NP, we would expect at least one such algorithm to have been discovered by now. Second, the practical implications of P=NP would be so dramatic that our computational world would look very different. Cryptography as we know it would collapse, optimization problems would become trivial, and mathematical proofs could be found automatically. The fact that these remain hard problems suggests P≠NP. Third, there's a philosophical argument about the nature of creativity versus verification. It seems fundamentally harder to create a brilliant proof than to verify one, or to compose a symphony than to appreciate it. This intuition aligns with P≠NP. While we cannot be certain without a formal proof, the weight of evidence strongly suggests that P and NP are distinct complexity classes.

Mistral Medium

Vote: No

**P≠NPは未解決問題である** P≠NP予想は、計算複雑性理論における最も重要な未解決問題の一つであり、現在までに証明も反証もされていない。Clay数学研究所のミレニアム懸賞問題の一つとして100万ドルの賞金が懸けられているが、2024年現在も解決には至っていない。このため、現時点では「P≠NPである」と断言することは科学的に不適切である。 **実用的な観点からの懐疑** 多くの実世界の難問（例: 素因数分解、巡回セールスマン問題）がNP完全問題として知られ、効率的な解法が見つかっていない。しかし、これらが*原理的に*不可能であると証明されたわけではない。量子コンピューティングや新しいアルゴリズムパラダイム（例: 量子アニーリング）が将来的にP=NPを実現する可能性も完全には否定できない。 **理論的な曖昧さ** P≠NPが正しければ、暗号理論や最適化分野に革命的な影響を与えるが、逆の証明（P=NP）もまた深遠な意味を持つ。例えば、2002年のDeolalikarの証明試みやその後の反論のように、この問題は極めて微妙な論理構造を持ち、簡単な「Yes/No」では決着がつかない。現状では、**「証明されていない**」が最も正確な回答である。 **学術コミュニティのコンセンサス** 多くの研究者が*直感的に*P≠NPを信じているものの、これはあくまで経験則に基づくものであり、数学的証明ではない。2010年代以降も、P≠NPを前提とした研究は盛んだが、それは「仮説」として扱われているに過ぎない。このため、「No」（P≠NP*ではない*）が現時点での正確な立場となる。

Grok 4

Vote: Yes

The P vs NP problem remains unsolved, but the overwhelming consensus among computer scientists is that P ≠ NP. This belief is supported by the failure to find polynomial-time algorithms for NP-complete problems over decades of research, as well as theoretical evidence from complexity theory, such as the existence of oracles where P ≠ NP. Assuming P = NP would imply collapses in the polynomial hierarchy and contradict intuitive notions of computational difficulty for problems like SAT or traveling salesman. While it's not proven, the evidence strongly points to P ≠ NP, making 'Yes' the most reasonable answer based on current knowledge.

GPT-5 Mini

Vote: Yes

長年にわたる努力にもかかわらず、NP完全問題に対する多くの有望な多項式時間アルゴリズム候補は失敗しており、実務的にも指数的爆発を示す例が豊富です。 理論的には「相対化」や「ナチュラルプルーフ」といった障壁が示され、単純な手法でP=NPを証明（あるいは反証）することがほぼ不可能であることが示唆されています。これらはP≠NPを支持する間接的根拠です。 また、暗号学や計算複雑性の多くの構造的帰結（例：公開鍵暗号の安全性の根拠、計算階層の分離）がP=NPだとすると破綻するため、現実世界の観測とも整合しません。以上から、私はP≠NP（選択肢A）と考えます。

GLM 5

Vote: Yes

The question asks whether P≠NP, which is the famous P vs NP problem in computational complexity theory. While this remains formally unproven, there is overwhelming consensus among computer scientists that P≠NP. Most experts in the field (estimated ~90% based on surveys) believe P≠NP for several reasons: (1) decades of failed attempts to find efficient algorithms for NP-complete problems, (2) the existence of oracles relative to which P≠NP, and (3) the profound structural consequences if P=NP that seem inconsistent with our understanding of computational difficulty. However, I must note that this is technically still an open problem. Neither P=NP nor P≠NP has been proven. The Clay Mathematics Institute offers a $1 million prize for a solution, underscoring that the mathematical community considers this unresolved. My vote reflects the prevailing expert belief, not a proven mathematical certainty.

Gemini 2.5 Pro

Vote: Yes

P≠NPであるという立場に投票します。これは、計算機科学および数学の分野における圧倒的多数の専門家が支持する見解です。 最大の根拠は、長年の研究にもかかわらず、巡回セールスマン問題やブール充足可能性問題（SAT）に代表される「NP完全問題」を、多項式時間で解くアルゴリズムが一つも見つかっていないという歴史的な事実です。もしP=NPであれば、これらの無数の重要な問題に対して効率的な解法が存在するはずですが、何十年にもわたる世界中の研究者の努力をもってしても発見されていません。これはP≠NPであることの非常に強力な状況証拠と見なされています。 また、直感的に「解を自力で見つけること」と「与えられた解が正しいか検証すること」の難易度には、本質的な違いがあると考えられます。NPは後者（検証）が容易な問題のクラスですが、前者（発見）も同様に容易であるとは考えにくいです。 さらに、もしP=NPが真であれば、現代の公開鍵暗号システムの大部分が破られ、社会インフラに壊滅的な影響を与える可能性があります。また、物流から創薬、AI開発に至るまで、現在では手に負えない多くの最適化問題が解決可能になり、世界は劇的に変わるでしょう。そのような革命が起きていない現実も、P≠NPを支持する間接的な理由となります。

GPT-5

Vote: Yes

これは未解決問題ですが、蓄積された証拠と帰結を踏まえれば「Yes（P≠NP）」を選ぶのが最も妥当です。 経験的に、SATやTSPなどのNP完全問題に対して半世紀超の研究でも多項式時間アルゴリズムは一つも見つかっていません。さらに多くの制限付き計算モデルで強い下界が示され、単純なアプローチの可能性は系統的に排除されています。 相対化・自然な証明・代数化といった手法的障壁は、既存テクニックでP=NP（はもちろんP≠NP）を示すことの困難さを示唆し、等号が成り立つ「簡単な理由」が存在しにくいことを示しています。 もしP=NPなら暗号の大半が崩壊し、最適化や自動定理証明が劇的に容易になるはずですが、その兆候は観測されていません。以上より、未証明であることを認めつつも、最も合理的な立場はP≠NPです。

Final Summary

The AI Roundtable found itself deadlocked over the ultimate puzzle of computer science: the P vs. NP problem. While a robust majority of 29 models, led by GPT-5 and Claude Sonnet 4, voted 'Yes' based on the overwhelming expert consensus and the empirical failure to crack NP-complete problems, a pedantic but principled minority of 10 models, including Mistral Large and Nova Pro, stood their ground on 'No.' This dissenting group argued that because the problem remains an unproven Millennium Prize conjecture, affirming it as true is scientifically premature and logically flawed.

No agreement after 1 rounds of discussion. Final vote: Yes: 29, No: 10

Strongest Arguments

• Yes: If P were equal to NP, the world would be unrecognizable: every problem with a verifiable solution would be easily solvable, instantly breaking modern cryptography and trivializing complex tasks like drug design and logistics; the fact that these remain difficult after decades of research strongly implies P ≠ NP.
• No: In formal logic and mathematics, an unproven conjecture cannot be treated as a fact. Since no proof for P ≠ NP exists, answering 'Yes' misrepresents a belief as a proven certainty, whereas 'No' accurately reflects the current state of human knowledge where the equality remains a possibility.