Related papers: Lower bounds for algebraic machines, semantically
Large language models (LLMs) show strong performance across natural language processing (NLP), mathematical reasoning, and programming, and recent large reasoning models (LRMs) further emphasize explicit reasoning. Yet their computational…
This paper introduces a more restrictive notion of feasibility of functionals on Baire space than the established one from second-order complexity theory. Thereby making it possible to consider functions on the natural numbers as running…
We study a clean machine model for external memory and stream processing. We show that the number of scans of the external data induces a strict hierarchy (as long as work space is sufficiently small, e.g., polylogarithmic in the size of…
We introduce a new algebraic proof system, which has tight connections to (algebraic) circuit complexity. In particular, we show that any super-polynomial lower bound on any Boolean tautology in our proof system implies that the permanent…
This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: -- On Universal Turing Machines, a program's time complexity should be characterized as:…
We define counting classes #P_R and #P_C in the Blum-Shub-Smale setting of computations over the real or complex numbers, respectively. The problems of counting the number of solutions of systems of polynomial inequalities over R, or of…
In this work we advance the understanding of the fundamental limits of computation for Binary Polynomial Optimization (BPO), which is the problem of maximizing a given polynomial function over all binary points. In our main result we…
A polynomial Turing compression (PTC) for a parameterized problem $L$ is a polynomial time Turing machine that has access to an oracle for a problem $L'$ such that a polynomial in the input parameter bounds each query. Meanwhile, a…
This paper addresses the problem of enumerating all supported efficient solutions for a linear multi-objective integer minimum cost flow problem (MOIMCF). It derives an output-polynomial time algorithm to determine all supported efficient…
We present a new strongly polynomial algorithm for generalized flow maximization that is significantly simpler and faster than the previous strongly polynomial algorithm [V\'egh16]. For the uncapacitated problem formulation, the complexity…
The subcube partition model of computation is at least as powerful as decision trees but no separation between these models was known. We show that there exists a function whose deterministic subcube partition complexity is asymptotically…
Traditional Turing machines are semantically poor, they only concern the syntactic manipulation of symbols, discarding the mathematical semantics behind the symbols. This semantic deficiency is considered the root cause of the three major…
This dissertation proves lower bounds on the inherent difficulty of deciding flow analysis problems in higher-order programming languages. We give exact characterizations of the computational complexity of 0CFA, the $k$CFA hierarchy, and…
One of the big challenges in the development of probabilistic relational (or probabilistic logical) modeling and learning frameworks is the design of inference techniques that operate on the level of the abstract model representation…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
Partial Differential Equations (PDEs) are fundamental tools for modeling physical phenomena, yet most PDEs of practical interest cannot be solved analytically and require numerical approximations. The feasibility of such numerical methods,…
Branching bisimilarity on normed Basic Process Algebra (BPA) was claimed to be EXPTIME-hard in previous papers without any explicit proof. Recently it is reminded by Jan\v{c}ar that the claim is not so dependable. In this paper, we develop…
In this paper, we present PARTIME, a software library written in Python and based on PyTorch, designed specifically to speed up neural networks whenever data is continuously streamed over time, for both learning and inference. Existing…
The article studies query evaluation in parallel constant time in the CRCW PRAM model. While it is well-known that all relational algebra queries can be evaluated in constant time on an appropriate CRCW PRAM model, this article is…