'z3' 검색 결과

Choose approaches for prime number problems, including primality testing, factorization, and prime distribution. The skill outlines relevant algorithms and theorems, with commands for symbolic calculation and checking mathematical claims.

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• Choosing a primality testing method
• Selecting a factorization approach
• Studying prime distribution and gaps

Plan solutions to modular arithmetic problems, which involve integer remainders. Choose methods for modular inverses, simultaneous congruences, powers, quadratic residues, and primitive roots, with example commands for symbolic calculations and checking mathematical claims.

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• Finding a modular inverse with the extended Euclidean algorithm
• Solving simultaneous congruences with the Chinese Remainder Theorem
• Simplifying powers using Euler's Theorem

Helps select graph algorithms for shortest paths, minimum spanning trees, network flow, and coloring. Provides decision guides and example commands for symbolic calculations and checking mathematical properties.

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• Choosing a shortest path algorithm
• Planning a minimum spanning tree solution
• Setting up network flow equations

Find numerical solutions where a function equals zero. The skill helps choose a method based on known intervals and available derivatives, then guides SciPy implementation, searches for multiple solutions, and checks accuracy and valid ranges.

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• Finding a solution within a known interval
• Choosing a method based on derivative availability
• Solving systems of nonlinear equations

Choose approaches to Hilbert space problems in functional analysis using orthogonal decomposition, projection, and representation theorems. The skill provides a decision tree and command examples for inner product calculations and proof tasks.

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• Choosing an approach to Hilbert space exercises
• Studying orthogonal decomposition and projection
• Working through the Riesz representation theorem

Plan solutions to Banach space problems in functional analysis. Work through completeness, meaning Cauchy sequences converge, and select major theorems to guide arguments about extending linear functionals, open mappings, and bounded operators.

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• Planning a proof that a normed space is complete
• Choosing a theorem for extending a linear functional
• Studying open mappings and bounded inverses

Work through first-order ordinary differential equations by classifying their form and choosing a solution method. The skill also covers numerical initial-value problems, checking solutions against the equation and conditions, and examining equilibrium stability.

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• Choosing a method for a first-order differential equation
• Computing a numerical solution with initial values
• Checking a solution against the equation and conditions

Investigate whether a complex function is analytic, meaning it has a local power series representation. The skill guides derivative checks, Cauchy–Riemann equations, power series and convergence radii, plus ways to explore extension beyond the original domain.

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• Checking where a complex function is analytic
• Verifying the Cauchy–Riemann equations
• Finding a power series and its convergence radius

Solve optimization problems with equality constraints, inequalities, or variable bounds. Guides method selection, symbolic equations, and optimality checks, with SciPy examples for finding numerical solutions that respect the stated constraints.

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• Classify constraints before choosing a solution method
• Solve equality-constrained problems with Lagrange multipliers
• Check KKT conditions for inequality constraints

Work through convex optimization problems by checking convexity, putting objectives and constraints into a standard form, and choosing a solver. The skill provides SciPy examples and outlines checks for constraint satisfaction and mathematical conditions used to assess optimality.

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• Checking whether an objective and its constraints are convex
• Putting a maximization problem into standard minimization form
• Choosing a solver for linear, quadratic, or semidefinite problems

Work through convergence problems in real analysis by identifying sequence and series types, choosing suitable tests, checking limits and bounds, and calculating sums when a series converges.

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• Choose a convergence test for a series
• Check sequence limits and inequality bounds
• Calculate the sum of a convergent series

Work through linear algebra problems involving vector spaces, from checking subspaces and linear independence to finding bases, dimensions, and coordinate changes. The skill connects each task to symbolic calculation or proof scripts for checking the results.

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• Checking whether a set is a vector subspace
• Testing vectors for linear independence
• Finding a basis and dimension

Work through Lebesgue measure problems, which concern assigning sizes to sets. The skill organizes approaches to outer measure, measurability criteria, translation invariance, countable additivity, and approximation by compact or open sets, with supporting tool command examples.

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• Review outer measure defined through interval covers
• Study measurability using the Caratheodory criterion
• Organize proofs of basic Lebesgue measure properties

Study source coding, the information theory behind data compression. The skill guides problems involving Huffman codes, average code length, prefix-code constraints, arithmetic coding, and the tradeoff between compression rate and distortion, with calculation and proof command examples.

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• Construct Huffman codes from symbol probabilities
• Compare average code length with entropy
• Check code lengths using Kraft's inequality

Work through integration problems in measure theory by matching the problem's conditions to suitable theorems. The skill covers simple functions, exchanging limits and integrals, lower bounds, and changing integration order, with commands for symbolic calculations and proof tools.

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• Choosing a theorem for exchanging limits and integrals
• Checking conditions for changing integration order
• Finding lower bounds with Fatou's lemma

Validate vulnerability findings by checking code, reachable attack paths, observable test results, and realistic prerequisites. The workflow produces evidence-backed reports and assesses binary constraints for memory corruption issues before exploit development proceeds.

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• Verify vulnerability scanner findings
• Identify unreachable code and unrealistic prerequisites
• Assess exploitation constraints for memory corruption

Symbolic execution and constraint solving playbook. Use when solving CTF reversing challenges, recovering keys, bypassing checks, or automating binary analysis with angr, Z3, or Unicorn Engine.

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Performs symbolic execution to detect potential errors by exploring execution paths, solving path constraints, and generating test inputs. Use when you need to analyze code for bugs like null dereferences, division by zero, buffer overflows, or assertion violations. Also use to generate test inputs that exercise different code paths, find edge cases, or explore all reachable program states. Supports Python, Java, and C/C++ through manual symbolic execution techniques and integration with tools like KLEE, angr, Z3, and Symbolic PathFinder.

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Think and work like an expert Logician. Use when a task calls for Logician judgment. Reasons from syntax-versus-semantics and object-versus-metalanguage discipline, the ⊢/⊨ distinction, and matching each logic to its intended semantics through natural deduction and sequent calculus (cut-elimination, subformula property), compactness and Löwenheim–Skolem, forcing and diagonalization, and proof assistants (Lean 4/mathlib, Coq, Isabelle/HOL, Agda) with Z3/CVC5/Vampire/Mace4 automation while treating use–mention conflation, second-order misuse of compactness, mis-stated incompleteness hypotheses (ω-consistency vs consistency), and Gödel philosophical overreach as first-class failure modes.

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Think and work like an expert Formal Methods Researcher. Use when a task calls for Formal Methods Researcher judgment. Reasons from operational semantics and temporal logics through SPIN/TLA+/PRISM, Coq/Lean/Isabelle, Z3/CVC5, refinement and separation logic, vacuity and false-positive diagnosis, and Dafny/F* versus property-based testing boundaries.

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Think and work like an expert Computer Scientist. Use when a task calls for Computer Scientist judgment. Reasons from computational models, abstraction contracts, invariants, and measurable complexity through CLRS-grade algorithm analysis, impossibility results (FLP, CAP, NP-hardness), property-based and chaos testing, and formal tools (TLA+, Coq, Z3) while treating partial failure, race conditions, label leakage, and abstraction leaks like GC pauses and clock skew as first-class failure modes.

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Proves protocols and agent workflows with TLA+, P, Alloy, Z3, Dafny, or Lean. Use when proving protocols correct, writing TLA+ specs, or verifying LLM proofs.

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Portable Codebase Argus agent playbook for evidence-first multi-agent review of GitHub pull requests, CI failures, GitHub Actions logs, GitHub App webhook review, /argus PR comment commands, autofix branch planning, OpenAI/Claude/Gemini/Codex provider tribunals, downstream merge/rebase work, and long-lived fork sync against an upstream repository.

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Automate on-target verification of a program's logic by driving its RTT console with rttsh - write Lua scripts that exercise commands and assert responses, output and timing on real hardware. Use when asked to verify target-side behavior on board, build board-level checks for firmware features, or automate hardware test runs.

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