Related papers: Formal Verification of Minimax Algorithms
This paper has three main contributions to our understanding of fixed-depth minimax search: (A) A new formulation for Stockman's SSS* algorithm, based on Alpha-Beta, is presented. It solves all the perceived drawbacks of SSS*, finally…
Knuth and Moore presented a theoretical lower bound on the number of leaves that any fixed-depth minimax tree-search algorithm traversing a uniform tree must explore, the so-called minimal tree. Since real-life minimax trees are not…
This paper introduces a new paradigm for minimax game-tree search algo- rithms. MT is a memory-enhanced version of Pearls Test procedure. By changing the way MT is called, a number of best-first game-tree search algorithms can be simply and…
Formal software verification techniques are widely used to specify and prove the functional correctness of programs. However, nonfunctional properties such as time complexity are usually carried out with pen and paper. Inefficient code in…
The problem of mechanically formalizing and proving metatheoretic properties of programming language calculi, type systems, operational semantics, and related formal systems has received considerable attention recently. However, the dual…
In verification-aware languages, such as Dafny, despite their critical role, specifications are as prone to error as implementations. Flaws in specifications can result in formally verified programs that deviate from the intended behavior.…
Formal verification techniques aim at formally proving the correctness of a computer program with respect to a formal specification, but the expertise and effort required for applying formal specification and verification techniques and…
As machine learning systems are increasingly used to make real world legal and financial decisions, it is of paramount importance that we develop algorithms to verify that these systems do not discriminate against minorities. We design a…
The traditional approach to choosing moves in game-playing programs is the minimax procedure. The general belief underlying its use is that increasing search depth improves play. Recent research has shown that given certain simplifying…
In this paper, we present our ongoing work and initial results on the formal specification and verification of MiniMaple (a substantial subset of Maple with slight extensions) programs. The main goal of our work is to find behavioral errors…
This paper describes the formal verification of two Turing machines using the program verifier Dafny. Both machines are deciders, so we prove total correctness. They are typical first examples of Turing machines used in any course of…
Formal verification has the potential to drastically reduce software bugs, but its high additional cost has hindered large-scale adoption. While Dafny presents a promise to significantly reduce the effort to write verified programs, users…
Smale's alpha-theory uses estimates related to the convergence of Newton's method to give criteria implying that Newton iterations will converge quadratically to solutions to a square polynomial system. The program alphaCertified implements…
Certified verification of transformer attention requires bounding the softmax function over interval constraints on the pre-softmax scores. Existing verifiers relax softmax ndependently of the downstream objective, leaving avoidable slack.…
Verification of deep neural networks has witnessed a recent surge of interest, fueled by success stories in diverse domains and by abreast concerns about safety and security in envisaged applications. Complexity and sheer size of such…
Most practitioners use a variant of the Alpha-Beta algorithm, a simple depth-first pro- cedure, for searching minimax trees. SSS*, with its best-first search strategy, reportedly offers the potential for more efficient search. However, the…
Deep neural network (DNN) verification is an emerging field, with diverse verification engines quickly becoming available. Demonstrating the effectiveness of these engines on real-world DNNs is an important step towards their wider…
The proliferation of decentralized financial (DeFi) systems and smart contracts has underscored the critical need for software correctness. Bugs in such systems can lead to catastrophic financial losses. Formal verification offers a path to…
We study parallel algorithms for the minimisation and equivalence checking of Deterministic Finite Automata (DFAs). Regarding DFA minimisation, we implement four different massively parallel algorithms on Graphics Processing Units~(GPUs).…
With the rapid growth of machine learning, deep neural networks (DNNs) are now being used in numerous domains. Unfortunately, DNNs are "black-boxes", and cannot be interpreted by humans, which is a substantial concern in safety-critical…