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Verifying a Sequent Calculus Prover for First-Order Logic with Functions in Isabelle/HOL
We describe the design, implementation and verification of an automated theorem prover for first-order logic with functions. The proof search...
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Refinement of Parallel Algorithms Down to LLVM: Applied to Practically Efficient Parallel Sorting
We present a stepwise refinement approach to develop verified parallel algorithms, down to efficient LLVM code. The resulting algorithms’ performance...
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General Clauses for SAT-Based Proof Search in Intuitionistic Propositional Logic
In recent years some papers have addressed the problem of the validity in Intuitionistic Propositional Logic (IPL) using the approach proposed by...
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Gale-Shapley Verified
This paper presents a detailed verification of the Gale-Shapley algorithm for stable matching (or marriage). The verification proceeds by stepwise...
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Automated Generation of Geometry Proof Problems Based on Point Geometry Identity
The automated generation of geometry proof problems represents a burgeoning research domain in the realm of artificial intelligence, with significant...
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Formalized Functional Analysis with Semilinear Maps
Semilinear maps are a generalization of linear maps between vector spaces where we allow the scalar action to be twisted by a ring homomorphism such...
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Linear Resources in Isabelle/HOL
We present a formal framework for process composition based on actions that are specified by their input and output resources. The correctness of...
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Invariant relations for affine loops
Invariant relations are used to analyze while loops; while their primary application is to derive the function of a loop, they can also be used to...
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Sequent Calculi for Choice Logics
Choice logics constitute a family of propositional logics and are used for the representation of preferences, with especially qualitative choice logic ...
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Revisiting 2–3 red–black trees with a pedagogically sound yet efficient deletion algorithm: parity-seeking
Red–black (RB) trees are one of the most efficient variants of balanced binary search trees. However, they have often been criticized for being too...
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Schematic Program Proofs with Abstract Execution
We propose Abstract Execution , a static verification framework based on symbolic execution and dynamic frames for proving properties of schematic ...
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Distance-edge-monitoring sets of networks
It is important to be able to monitor the network and detect this failure when a connection (an edge) fails. For a vertex set M and an edge e of the...
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Exact distributed quantum algorithm for generalized Simon’s problem
Simon’s problem is one of the most important problems demonstrating the power of quantum algorithms, as it greatly inspired the proposal of Shor’s...
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New families of Laplacian borderenergetic graphs
Laplacian matrix and its spectrum are commonly used for giving a measure in networks in order to analyse its topological properties. In this paper,...
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Should Decisions in QCDCL Follow Prefix Order?
Quantified conflict-driven clause learning (QCDCL) is one of the main solving approaches for quantified Boolean formulas (QBF). One of the...
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Non-termination in Term Rewriting and Logic Programming
In this paper, we define two particular forms of non-termination, namely loops and binary chains , in an abstract framework that encompasses term...
