Common Objections (Addressed)
“The SAT solver market is too small.”
The pure SAT-solver licensing market today is roughly $1B.
That number is a red herring: it measures revenue generated by today's
solvers on today's workloads, a function of solver capability,
not of latent demand.
Consider the machine learning analog. In 2012 the commercial
neural-network market was a rounding error. Computer vision, NLP, audio,
robotics, drug discovery, and recommendation all relied on handcrafted
features and shallow classifiers, because deep-network training was
intractable at scale. Once GPU training became practical, ML did not
merely grow the 2012 market; it expanded into adjacent categories.
Those fields collectively became a much larger ML market.
A 10× SAT speedup could trigger a similar dynamic in industries that
currently accept heuristic output because more exact methods are too slow:
EDA placement and routing, supply-chain planning, quant order scheduling,
protein folding and drug design, compiler optimization, constraint-based
manufacturing scheduling. The addressable market is broader than
today's licensing pool because customers pay for quality, certainty,
auditability, and lower search cost.
“P ≠ NP, so this is fundamentally impossible.”
Echea does not claim P = NP as a theorem. That problem is formally
open, and nothing we are building depends on resolving it.
But the informal intuition behind this objection, "NP-hard
problems must remain intractable on practical instances",
is less absolute than it once appeared, and investors
should update accordingly.
First, the direct historical evidence. Since 1980,
SAT solvers have improved by roughly 10,000× on
industrially relevant instance classes. The CDCL revolution alone
delivered several orders of magnitude without touching P vs NP. These
gains came from exploiting structure in many real
instances of NP-hard problems that worst-case complexity theory
does not characterize. The trend is still active.
Second, the recent AI signal. The rise of
advanced AI systems provides an additional, and in our view
under-appreciated, empirical update. Modern large models,
which are bounded-size neural networks executing in polynomial
forward-pass time, are now demonstrably solving or tightly
approximating problems once considered to require exponential search:
ad-hoc theorem proving, multi-step planning, combinatorial puzzle
solving, code synthesis, and rough formal proofs. This is
not a formal proof of P = NP. Worst-case complexity is
untouched, and the theoretical question remains open. But it
suggests that the practical
frontier between "polynomial" and "exponential" is far less strict
than classical intuition suggested. Problems previously assumed to
require exhaustive reasoning are increasingly being approximated or
solved on practical instances by bounded systems.
The rational update. Given recent AI progress, the
informal prior that "NP-hard means practically intractable" should be
treated with more nuance. Echea is not betting on a proof of P = NP.
We are betting that a commercially meaningful fraction of hard practical
instances has exploitable structure, and that better structural tools can
make those workloads more exact, verifiable, and cheaper to solve.
“Stochastic methods / ML are winning. Why go deterministic?”
Heuristics and stochastic methods dominate today's AI landscape
because rigorous alternatives did not exist at scale. That is not
an argument against building rigorous alternatives, it is the
reason to build them.
Entire categories are difficult to serve with stochastic methods alone:
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Chip verification cannot tolerate probabilistic
correctness. A fabbed logic bug on a 3nm node costs $100M+ to
correct. Chip designers verify with SAT and SMT solvers, and
will continue to.
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Safety-critical systems (aerospace, medical
devices, autonomous vehicles) increasingly require formal
proofs rather than statistical guarantees. The FAA does not
certify "trained probabilistic landing."
-
Cryptographic assurance is built on exact
computation, not approximation.
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Reliability analysis and probabilistic inference
in structured domains reduce directly to #SAT. Stochastic
sampling gives noisy estimates; #SAT gives exact counts.
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AI alignment itself increasingly benefits from formal
verification of agent behaviour, policy bounds, and value
specifications. As models become more capable, probabilistic
behavioural testing becomes less sufficient; the field will need
stronger deterministic checks than it currently has.
Stochastic and deterministic methods are complementary, not
competitive. Echea is building a deterministic layer for the stack:
the part that can make selected workflows more exact, verifiable,
and cost-efficient at industrial scale.
“Big labs will just build this themselves.”
They could, but their current incentives and staffing are pointed
elsewhere, and the pattern is well documented.
The frontier labs (OpenAI, Anthropic, DeepMind, Meta AI, xAI) have
publicly committed enormous capital to scaling stochastic
pre-training. Their technical leadership, compute, and roadmaps are
structured around improving neural-network training efficiency,
not around applying algebraic graph theory and algebraic topology
to model counting. Their research output in #SAT and algebraic
combinatorics appears limited relative to their work on stochastic scaling.
Even if a frontier lab reallocated a pod to this area tomorrow,
they would face a steep staffing problem. The combination of deep
combinatorial and #SAT expertise, fluency in algebraic graph
theory / spectral methods / algebraic topology, and CUDA-level
systems engineering for industrial-scale solver implementation is
exceptionally rare. Most people with the first two skills are in
academia; most people with the third are at chip companies or
high-frequency trading firms. Our team spans all three: Harvard CS
theory, MIT research on NP-Complete protein folding, Stanford PhD
in Math and CS, Etched chip-design silicon, and Google Connectomics
pretraining systems experience. Leslie Valiant as academic advisor
attracts downstream research talent into our orbit rather than
theirs.
Historically, the large labs have acquired rather
than built specialized capability: Google's DeepMind
acquisition, Nvidia's Mellanox, Intel's Mobileye. This sector could
follow a similar pattern if the technical milestones are achieved.
“This belongs in academia, not a startup.”
Every piece of industrial optimization software shipping today
descended from academic research but was built outside the academy.
CUDA came from Nvidia, not Stanford. Gurobi,
the dominant commercial linear and integer programming solver, with
revenue approaching $1B, was commercialized by engineers who
left academia for exactly this reason. IBM's CPLEX, FICO's Xpress,
Mosek: the same story.
Academic groups publish algorithms; they do not build industrial-scale
developer ecosystems, customer-facing toolchains, benchmark suites,
or tightly integrated commercial support. Universities do not
optimize for integration; their incentive structures favour
publication. The value in this space, and the gap, is
productizing mathematical breakthroughs at scale. A startup is a
practical vehicle, and Echea is structured to operate between
academic research and industrial deployment.
“Heuristic solvers are good enough.”
"Good enough" in this sector can still leave large amounts of
value on the table. Industries using heuristic optimization often
pay a measurable efficiency tax:
-
In EDA, current heuristic placement and routing
tools can leave silicon area, wire length, and power on
the table versus stronger optimization. On a flagship TSMC 3nm
tape-out costing $300M+, a 3% area improvement is $9M+ per chip
family, and a fab ships many families per year.
-
In quant trading, heuristic order-scheduling
can lose basis points of alpha at tier-1 firms, which can be
material in absolute terms at a $100B AUM shop. It also often
cannot produce the deterministic proof trails that
regulators increasingly require.
-
In logistics and manufacturing scheduling,
heuristic operations-research software (the core of the
Gurobi/CPLEX market) is priced at low six figures per seat
precisely because small percentage improvements in schedule
quality translate into meaningful top-line gains.
-
In drug design, combinatorial search over
chemical space is constrained by heuristic methods; enlarging
the searchable region by even an order of magnitude materially
can increase hit rates in lead discovery.
"Good enough" is often the marketing of current incumbents. Each
measurable point of efficiency, cost, or auditability can become a
revenue opportunity for better solvers.
“#P-complete problems are decades old and nobody has cracked them. Why would you?”
Historically, many meaningful breakthroughs on #P-complete and
adjacent counting problems have come from one mathematical object:
the determinant
and its surprising algebraic generalizations. The determinant is
the canonical example of a polynomial-time-computable function that
unexpectedly captures rich combinatorial counting structure,
and its generalizations have been responsible for several of
the field's celebrated positive results.
Consider the precedent. The matrix-tree theorem
(Kirchhoff, 1847) reduces counting spanning trees of a graph,
a combinatorial object, to the determinant of the Laplacian
matrix, giving a polynomial-time algorithm for a problem that looks
exponential on its face. The FKT algorithm
(Fisher, Kasteleyn, Temperley) solves counting perfect matchings in
planar graphs, which is #P-complete in the general case,
in polynomial time, using the Pfaffian (a determinant-like object).
Holographic algorithms (Valiant, 2004) generalize this
further: families of #P-complete problems can collapse to polynomial
time when the problem's structure admits an encoding into matchgates
and Pfaffians. Holant problems and matchgate
tractability extend the framework still further.
The pattern is consistent: many surprising positive results in
#P-complete counting come from determinants, Pfaffians,
and their algebraic generalizations. And those generalizations
continue to appear. Recent work on spectral characterizations of graph
polynomials, algebraic and topological invariants from cohomology
applied to constraint satisfaction, and deep connections between
#SAT, permanents, and tensor decompositions are actively opening new
structural hooks into the #P-complete landscape.
Our team includes Leslie Valiant, the Turing laureate who
defined the #P complexity class, proved the #P-completeness of the
permanent, and invented holographic algorithms. That is not a
coincidence. The intellectual lineage Echea is pursuing is
part of the lineage that has produced important
breakthroughs in this field, and that lineage is still actively
generalizing. The existing body of work on determinants and their
extensions is not a dead end; it remains a productive
research programme in computational complexity and a natural place
to search for the next practical breakthrough.
“Sales cycles in EDA and finance are long.”
Long sales cycles are real. EDA procurement runs 9–18 months;
finance procurement runs 6–12 months. The business is
designed to manage them.
The founder network is already engaged with tier-1 targets through
Etched, prior Harvard and Google relationships, and Leslie
Valiant's academic network. Warm introductions exist today.
Pilots are priced asymmetrically against downstream economic value,
not against cost: a pilot can be small relative to the value at
stake per chip tape-out or trading workflow. Companies selling into
conservative sectors often manage long cycles through direct technical
engagement, reference customers, and founder-led sales. Echea is
structured similarly.
In parallel, the research publication track, first paper
shipped, second in progress, is designed to generate pull
from adjacent industries. Academic and industrial researchers will
bring the technology to their employers as citations and benchmark
results accumulate.
