{'fraction_non_alphanumeric': 0.0310192023633678, 'fraction_numerical': 0.007877892663712457, 'mean_word_length': 4.889855072463768, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Synthesis under Assumptions

We consider the following elusive question which has generated a lot of ad hoc research: In synthesis/planning, which constraints on traces are environment assumptions? We propose to view assumptions as sets of strategies and not, as is typical, as sets of traces, even for assumptions expressed as linear-temporal formulas on traces. This shift in perspective allows us to give a principled and conceptually clear answer to this question, as well as to reuse results and techniques for synthesis in order to solve synthesis under assumptions. Context. Reasoning about actions and planning concerns the representation of a dynamic system (Reiter 2001). Such a representation corresponds to knowledge that the agent has of the environment. In devising plans, the agent takes advantage of such a representation of the world. In other words, the agent assumes that the environment works in a certain way, and exploits such an assumption in devising its plans. A question immediately comes to mind: What is an environment assumption? Obviously the planning domain itself (including the initial state) with its preconditions and effects is an environment assumption. That is, as long as the agent sticks to its preconditions, the environment acts as described by the domain. So, the agent can exploit the effect of its actions in order to reach a certain goal (state of affairs). It is also common to assume the domain is fair, cf. (D’Ippolito, Rodrı́guez, and Sardiña 2018), or more generally that the environment’s behavior is restricted by trajectory constraints, often expressed in LTL, cf. (De Giacomo et al. 2016; Bonet et al. 2017). But, is any kind of formula on the fluents and actions of the domain a possible trajectory constraint for the environment? The answer is obviously “no” — indeed, consider a formula expressing that eventually a certain possible action must actually be performed — the agent may decide not to do it. But then we ask: Which linear-time specifications are environment as-