Publications by Mika Tapani Göös

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We exhibit an unambiguous k-DNF formula that requires CNF width (Omega) over tilde (k(2)), which is optimal up to logarithmic factors. As a consequence, we get a near-optimal solution to the Alon-Saks-Seymour problem in graph theory (posed in 1991), which ...

We exhibit a total search problem with classically verifiable solutions whose communication complexity in the quantum SMP model is exponentially smaller than in the classical two-way randomized model. Our problem is a bipartite version of a query complexit ...

We show that Cutting Planes (CP) proofs are hard to find: Given an unsatisfiable formula F, It is -hard to find a CP refutation of F in time polynomial in the length of the shortest such refutation; and unless Gap-Hitting-Set admits a nontrivial algorithm, ...

Suppose we have randomized decision trees for an outer function f and an inner function g. The natural approach for obtaining a randomized decision tree for the composed function (f∘ gⁿ)(x¹,…,xⁿ) = f(g(x¹),…,g(xⁿ)) involves amplifying the success probabili ...

Simon (1998) proved that it is impossible to construct collision-resistant hash functions from one-way functions using a black-box reduction. It is conjectured more generally that one-way functions do not imply, via a black-box reduction, the hardness of a ...

We use results from communication complexity, both new and old ones, to prove lower bounds for unambiguous finite automata (UFAs). We show three results. 1) Complement: There is a language L recognised by an n-state UFA such that the complement language ̅L ...

We give a new characterization of the Sherali-Adams proof system, showing that there is a degree-d Sherali-Adams refutation of an unsatisfiable CNF formula C if and only if there is an ε > 0 and a degree-d conical junta J such that viol_C(x) - ε = J, where ...

For any unsatisfiable CNF formula F that is hard to refute in the Resolution proof system, we show that a gadget-composed version of F is hard to refute in any proof system whose lines are computed by efficient communication protocols-or, equivalently, tha ...

We show that algebraic proofs are hard to find: Given an unsatisfiable CNF formula F, it is NP-hard to find a refutation of F in the Nullstellensatz, Polynomial Calculus, or Sherali-Adams proof systems in time polynomial in the size of the shortest such re ...

We show EOPL = PLS \cap PsansP \sansP AD. Here the class EOPL consists of all total search problems that reduce to the END -OF -POTENTIAL -LINE problem, which was introduced in the works by Hub'acv \ek and Yogev (SICOMP 2020) and Fearnley et al. (JCSS 202 ...

Can every n-bit boolean function with deterministic query complexity k≪ n be restricted to O(k) variables such that the query complexity remains ω(k)? That is, can query complexity be condensed via restriction? We study such hardness condensation questions ...

We survey lower-bound results in complexity theory that have been obtained via newfound interconnections between propositional proof complexity, boolean circuit complexity, and query/communication complexity. We advocate for the theory of total search prob ...

Every known communication problem whose randomized communication cost is constant (independent of the input size) can be reduced to 𝑘-Hamming Distance, that is, solved with a constant number of deterministic queries to some 𝑘-Hamming Distance oracle. We ex ...

Aaronson (STOC 2010) conjectured that almost k-wise independence fools constant-depth circuits; he called this the generalised Linial-Nisan conjecture. Aaronson himself later found a counterexample for depth-3 circuits. We give here an improved counterexam ...

We show that computing the majority of n copies of a boolean function g has randomised query complexity R(Maj∘gⁿ) = Θ(n⋅R ̅_{1/n}(g)). In fact, we show that to obtain a similar result for any composed function f∘gⁿ, it suffices to prove a sufficiently stro ...

We exhibit a monotone function computable by a monotone circuit of quasipolynomial size such that any monotone circuit of polynomial depth requires exponential size. This is the first size–depth tradeoff result for monotone circuits in the so-called superc ...

We present a top-down lower-bound method for depth-4 boolean circuits. In particular, we give a new proof of the well-known result that the parity function requires depth-4 circuits of size exponential in n(1/3). Our proof is an application of robust sunfl ...

Mika Tapani Göös

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Unambiguous DNFs and Alon-Saks-Seymour

Quantum Communication Advantage in TFNP

Automating cutting planes is NP-hard

When Is Amplification Necessary for Composition in Randomized Query Complexity?

One-Way Functions vs. TFNP: Simpler and Improved

Lower Bounds for Unambiguous Automata via Communication Complexity

On Semi-Algebraic Proofs and Algorithms

Monotone Circuit Lower Bounds from Resolution

Automating Algebraic Proof Systems Is NP-Hard

Further Collapses in TFNP

Hardness Condensation by Restriction

Proofs, Circuits, and Communication

Constant-Cost Communication Is Not Reducible to k-Hamming Distance

Generalised Linial-Nisan Conjecture Is False for DNFs

A Majority Lemma for Randomised Query Complexity

Supercritical Tradeoffs for Monotone Circuits

Top-Down Lower Bounds for Depth-Four Circuits

A Lower Bound for Sampling Disjoint Sets

Extension Complexity of Independent Set Polytopes

Separations in Proof Complexity and TFNP