Effective and efficient reasoning in adversarial environments is important for many real-world applications ranging from cybersecurity to military operations. Deliberative reasoning techniques, such as Automated Planning, often restrict to static environments where only an agent can make changes by its actions. On the other hand, such techniques are effective and can generate non-trivial solutions. To explicitly reason in environments with an active adversary such as zero-sum games, the game-theoretic framework such as the Double Oracle algorithm can be leveraged. In this paper, we leverage the notions of critical and adversary actions, where critical actions should be applied before the adversary ones. We propose heuristics that provide a guidance for planners about what (critical) actions and in which order have to be applied in a good plan. We empirically evaluate our approach in terms of quality of generated strategies (by leveraging Double Oracle) and CPU time required to generated such strategies.
For every linear binary code C, we construct a geometric triangular configuration so that the weight enumerator of C is obtained by a simple formula from the weight enumerator of the cycle space of . The triangular configuration thus provides a geometric representation of C which carries its weight enumerator. This is the first step in the suggestion by M. Loebl, to extend the theory of Pfaffian orientations from graphs to general linear binary codes. Then we carry out also the second step by constructing, for every triangular configuration , a triangular configuration and a bijection between the cycle space of and the set of the perfect matchings of .
We say that a linear code C over a field F is triangular representable if there exists a two dimensional simplicial complex ∆ such that C is a punctured code of the kernel ker ∆ of the incidence matrix of ∆ over F and there is a linear mapping between C and ker ∆ which is a bijection and maps minimal codewords to minimal codewords. We show that the linear codes over rationals and over GF (p), where p is a prime, are triangular representable. In the case of finite fields, we show that this representation determines the weight enumerator of C. We present one application of this result to the partition function of the Potts model.On the other hand, we show that there exist linear codes over any field different from rationals and GF (p), p prime, that are not triangular representable. We show that every construction of triangular representation fails on a very weak condition that a linear code and its triangular representation have to have the same dimension.2000 MSC: 05C65, 94B05, 90C27, 55U10
Effective plan generation in adversarial environments has to take into account possible actions of adversary agents, i.e., the agent should know what the competitor will likely do.
In this paper we propose a novel approach for estimating strategies of the adversary, sampling actions that interfere with the agent's ones. The estimated competitor strategies are used in plan generation by considering that agent's actions have to be applied prior to the ones of the competitor, whose estimated times dictate the agent's deadlines. Missing these deadlines entails additional plan cost.
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