arXiv subjects

Sualeh Asif

Publications and source records attributed to Sualeh Asif.

5 recordsLinked to original sources

arXiv2026

Composer 2 Technical Report

Composer 2 is a specialized model designed for agentic software engineering. The model demonstrates strong long-term planning and coding intelligence while maintaining the ability to efficiently solve problems for interactive use. The model is trained in two phases: first, continued pretraining to improve the model's knowledge and latent coding ability, followed by large-scale reinforcement learning to improve end-to-end coding performance through stronger reasoning, accurate multi-step execution, and coherence on long-horizon realistic coding problems. We develop infrastructure to support training in the same Cursor harness that is used by the deployed model, with equivalent tools and structure, and use environments that match real problems closely. To measure the ability of the model on increasingly difficult tasks, we introduce a benchmark derived from real software engineering problems in large codebases including our own. Composer 2 is a frontier-level coding model and demonstrates a process for training strong domain-specialized models. On our CursorBench evaluations the model achieves a major improvement in accuracy compared to previous Composer models (61.3). On public benchmarks the model scores 61.7 on Terminal-Bench and 73.7 on SWE-bench Multilingual in our harness, comparable to state-of-the-art systems.

cs.SE↗

arXiv2022

PSPACE-completeness of Pulling Blocks to Reach a Goal

We prove PSPACE-completeness of all but one problem in a large space of pulling-block problems where the goal is for the agent to reach a target destination. The problems are parameterized by whether pulling is optional, the number of blocks which can be pulled simultaneously, whether there are fixed blocks or thin walls, and whether there is gravity. We show NP-hardness for the remaining problem, Pull?-1FG (optional pulling, strength 1, fixed blocks, with gravity).

cs.CC↗

arXiv2021

Computing L-Polynomials of Picard curves from Cartier-Manin matrices

We study the sequence of zeta functions $Z(C_p,T)$ of a generic Picard curve $C:y^3=f(x)$ defined over $\mathbb{Q}$ at primes $p$ of good reduction for $C$. We define a degree 9 polynomial $ψ_f\in \mathbb{Q}[x]$ such that the splitting field of $ψ_f(x^3/2)$ is the $2$-torsion field of the Jacobian of $C$. We prove that, for all but a density zero subset of primes, the zeta function $Z(C_p,T)$ is uniquely determined by the Cartier-Manin matrix $A_p$ of $C$ modulo $p$ and the splitting behavior modulo $p$ of $f$ and $ψ_f$; we also show that for primes $\equiv 1 \pmod{3}$ the matrix $A_p$ suffices and that for primes $\equiv 2 \pmod{3}$ the genericity assumption on $C$ is unnecessary. An element of the proof, which may be of independent interest, is the determination of the density of the set of primes of ordinary reduction for a generic Picard curve. By combining this with recent work of Sutherland, we obtain a practical deterministic algorithm that computes $Z(C_p,T)$ for almost all primes $p \le N$ using $N\log(N)^{3+o(1)}$ bit operations. This is the first practical result of this type for curves of genus greater than 2.

math.NT↗

arXiv2020

Arithmetic Expression Construction

When can $n$ given numbers be combined using arithmetic operators from a given subset of $\{+, -, \times, ÷\}$ to obtain a given target number? We study three variations of this problem of Arithmetic Expression Construction: when the expression (1) is unconstrained; (2) has a specified pattern of parentheses and operators (and only the numbers need to be assigned to blanks); or (3) must match a specified ordering of the numbers (but the operators and parenthesization are free). For each of these variants, and many of the subsets of $\{+,-,\times,÷\}$, we prove the problem NP-complete, sometimes in the weak sense and sometimes in the strong sense. Most of these proofs make use of a "rational function framework" which proves equivalence of these problems for values in rational functions with values in positive integers.

cs.CC↗

arXiv2020

Tetris is NP-hard even with $O(1)$ rows or columns

We prove that the classic falling-block video game Tetris (both survival and board clearing) remains NP-complete even when restricted to 8 columns, or to 4 rows, settling open problems posed over 15 years ago [BDH+04]. Our reduction is from 3-Partition, similar to the previous reduction for unrestricted board sizes, but with a better packing of buckets. On the positive side, we prove that 2-column Tetris (and 1-row Tetris) is polynomial. We also prove that the generalization of Tetris to larger $k$-omino pieces is NP-complete even when the board starts empty, even when restricted to 3 columns or 2 rows or constant-size pieces. Finally, we present an animated Tetris font.

cs.CC↗