{"id":"6957f7ef-45d0-4531-9e81-969296776ce4","arxiv_id":"2511.12974","paper_version":3,"verdict":"REJECT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"A formal extension of stochastic activity networks with explicit control actions, equipped with automata semantics, policy hierarchies, and a claimed reduction to CTMDPs, but with numerous unsupported proofs.","lead":"This paper defines Controlled Stochastic Activity Networks, a formal model that adds policy-driven control actions to stochastic activity networks, and develops automata-theoretic semantics, policy taxonomy, and language hierarchies for it. It claims the framework generalizes continuous-time Markov decision processes, which would matter for verification of safety-critical systems where timing, probability, and control interact.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Claimed CTMDP generalization fails: Definition 5.16 forces λ(q,c) to be independent of c, so general CTMDPs with action-dependent rates cannot be represented.","rationale":"The reader identified Proposition 5.17 and the normalization Σ_{q'}P(q,a,c,q')=1 as the fragile spot; this is the right location. However, the more precise problem is not merely an unproved isomorphism. Definition 5.16, combined with the normalization, makes the CMA-to-CTMDP map land in the strict subclass of CTMDPs whose exit rate is independent of the control action. A standard CTMDP may have rates that genuinely depend on the chosen action, and such a model has no CMA preimage. Since the abstract promises a unified framework that generalizes CTMDPs, this mathematical obstruction is directly load-bearing. The concern is not about the existence of an isomorphism proof but about the truth of the claimed subsumption; this strengthens, rather than weakens, the reader's REJECT. Other issues raised by the reader remain plausible, but this single counterexample is sufficient to invalidate the central contribution as stated. The verdict should remain REJECT; no verdict change is needed.","tokens_in":45748,"tokens_out":16561,"duration_ms":159691,"concrete_test":"Take the one-state CTMDP D with Q={q}, C={c₁,c₂}, λ(q,c₁)=1, λ(q,c₂)=10, and P(q,c₁,q)=P(q,c₂,q)=1. Suppose a CMA W=(Q,A,C,P,Q₀,σ) represents D via Definition 5.16. Then λ(q,c₁)=Σ_a σ(q,a)Σ_{q'}P(q,a,c₁,q')=Σ_a σ(q,a), and identically λ(q,c₂)=Σ_a σ(q,a), so λ(q,c₁)=λ(q,c₂), contradicting 1≠10. Thus no such CMA exists. This is an analytic counterexample; re-deriving Definition 5.16 from Definitions 4.2 and 5.12 confirms that the normalization forces the rate independence.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that Controlled SANs generalize CTMDPs fails at Definition 5.16. In a CMA (Definition 5.12), rates σ(q,a) depend only on state and activity, not on control action. Moreover, Definition 4.2 requires Σ_{q'} P(q,a,c,q') = 1 for every (q,a,c). Substituting into Definition 5.16 gives λ(q,c) = Σ_a σ(q,a) · Σ_{q'} P(q,a,c,q') = Σ_a σ(q,a), which is independent of c. Hence every CTMDP obtained from a CMA satisfies λ(q,c₁) = λ(q,c₂) for all c₁,c₂. But Definition 5.15 allows arbitrary action-dependent rates. For example, a one-state CTMDP with C={c₁,c₂}, λ(q,c₁)=1, λ(q,c₂)=10, P(q,cᵢ,q)=1 has no preimage under Definition 5.16. At best the construction covers a strict subclass of CTMDPs with control-independent exit rates. Proposition 5.17, even if proved, cannot repair this: state-process isomorphism would relate CMAs only to that subclass, not to general CTMDPs. The paper's main claim that Controlled SANs generalize CTMDPs therefore fails as stated.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces Controlled Stochastic Activity Networks (Controlled SANs), an extension of classical SANs in which timed activities are paired with explicit control actions chosen by policies. It presents a layered semantic hierarchy: controlled automata for nondeterministic behavior, controlled probabilistic automata for discrete probabilistic behavior, and controlled stochastic automata for continuous-time behavior. For each layer it defines policy classes (memoryless, finite-memory, stack-augmented, tape-augmented, history-dependent) and claims a strict expressiveness hierarchy over accepted languages, as well as closure and decidability results. It also claims that the framework generalizes DTMDPs and CTMDPs through representation theorems, and that any computable controlled automaton is realizable by a computable controlled activity network (Theorem 3.13, with a proof in Appendix A).","tokens_in":46087,"tokens_out":7360,"duration_ms":64437,"significance":"If the stated results were fully established, the paper would provide a genuinely unifying automata-theoretic framework for control, nondeterminism, probabilistic branching, and stochastic timing, with policy-based analysis and language-theoretic expressiveness classifications. The ambitions are substantial and the high-level structure is plausible: the policy hierarchy is a natural lifting of classical automata-theoretic memory hierarchies, and Theorem 3.13's reliance on the Turing universality of extended Petri nets is a credible strategy. The paper is also honest about many proof sketches and about the distinction between uniform and standard closure. However, the current manuscript contains load-bearing technical errors in the claimed DTMDP and CTMDP representations, and several central hierarchy statements are supported only by sketches or circular references. These issues must be resolved before the framework's advertised generality can be accepted.","major_comments":[{"comment":"The claimed generalization of CTMDPs is invalid as stated. In Definition 5.16, λ(q,c) = Σ_a σ(q,a) · Σ_{q'} P(q,a,c,q'). By Definition 4.2, Σ_{q'} P(q,a,c,q')=1 for every (q,a,c), so λ(q,c) = Σ_a σ(q,a), which is independent of c. Thus only CTMDPs whose total exit rate does not depend on the control action can be represented. A one-state CTMDP with λ(q,c1)=1 and λ(q,c2)=10 has no preimage. Proposition 5.17, even if proved, would only establish isomorphism to this restricted subclass, not to general CTMDPs. The abstract and Section 5's claim that Controlled SANs generalize CTMDPs is therefore not supported.","section":"§5.16–5.17"},{"comment":"The DTMDP representation of a controlled probabilistic automaton is also incorrect. Definition 4.40 sets P'(q,c,q') = Σ_{a∈A} P(q,a,c,q'). Since Definition 4.2 normalizes Σ_{q'} P(q,a,c,q')=1 for each (q,a,c), we get Σ_{q'} P'(q,c,q') = |A|, which violates the DTMDP normalization required in Definition 4.39 unless |A|=1. Proposition 4.41, which asserts an isomorphism of state processes, is stated without proof and appears to depend on this invalid construction. This undermines the paper's claim that controlled probabilistic automata generalize DTMDPs.","section":"§4.40–4.41"},{"comment":"The main expressiveness hierarchy results are supported only by proof sketches. Proposition 3.23 explicitly defers to the proof sketch of Theorem 3.29, and Theorem 3.29's proof is itself a sketch relying on examples such as {a^n b^n} and {a^n b^n c^n} without a formal construction showing that no policy in the lower class can accept those languages across all plants. The probabilistic analogues (Theorems 4.19 and 4.33) are likewise asserted by analogy. Since these hierarchies are a central contribution, full proofs or precise citations are needed, not just sketches.","section":"§3.29, §4.19, §4.33"},{"comment":"Proposition 3.31's witness argument is not generally valid. The proof assumes that a finite-memory controller enforcing L_p = (a^p)* 'necessarily counts steps mod p', and then derives a controller for L_{p^2}; but a controlled automaton S need not have the structural ability to emit 'a' and 'terminate' as assumed. The construction of L_{p^2} depends on properties of the plant that are not guaranteed by Definition 3.17. Thus the claimed non-realizability of the prime family by any single S is not established.","section":"§3.31"}],"minor_comments":[{"comment":"The type of a memoryless policy is given as π:Q→C, but the execution condition ci−1=π(hi) applies π to histories hi=(q0,a0)...(qi−1,ai−1). This is a type mismatch; clarify that the intended argument is the current state (or reindex appropriately).","section":"§3.15"},{"comment":"Definition 4.13 writes Prπ(ρ) with π(hi+1)(c), but memoryless probabilistic policies are defined as π:Q→Dist(C), which cannot accept a history argument. This notational inconsistency appears throughout Section 4 and should be fixed.","section":"§4.13"},{"comment":"Several equalities in Proposition 4.31 appear to be mislabeled: L^{ω,θ}_{Stack}(Uω) is equated with L^{ω,θ}_{H}(U'ω), and L^{ω,θ}_{Tape}(Uω) with L^{ω,θ}_{H}(U'ω), which is not the claimed bisimulation invariance. Check the indices.","section":"§4.31"},{"comment":"Definition 5.5 has tautological-looking lines: 'for any q∈Q and a∈A, F(.|q,a)=F(.|q,a), ρ(q,a)=ρ(q,a), Π(q,a)=Π(q,a)'. This should be a transfer of the stochastic network parameters to the realized automaton state, not an equality of the same symbols.","section":"§5.5"},{"comment":"Definition 4.9 says 'two equivalent controlled automata' but should refer to controlled probabilistic automata; the runs and policies are from U and M′, so the terminology is inconsistent.","section":"§4.9"},{"comment":"There are numerous typos and inconsistently rendered formulas (e.g., 'instatntaneous', 'contol', missing parentheses, mangled set notation such as P(2^{A*}) and duplicated Theorem 4.19/4.20). A careful proofreading pass is needed.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is unusually broad and appears to be an early draft: many central results are sketches, and two of the three representation theorems (DTMDP and CTMDP) contain concrete normalization errors. The CTMDP issue in particular looks fatal to the abstract's 'generalize CTMDPs' assertion as currently written, though it is repairable by making the enabling rate depend on the control action and re-proving the correspondence. If the authors are willing to make that substantive change and supply full proofs for the hierarchy claims, a revised version could be worth another round of review. As it stands, however, the paper overstates its results."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things you should know. First, the central claim that Controlled SANs generalize CTMDPs does not hold as written. Definition 5.16 defines lambda(q,c) = sum_a sigma(q,a) * sum_{q'} P(q,a,c,q'), and Definition 4.2 forces sum_{q'} P(q,a,c,q') = 1 for every (q,a,c). So lambda(q,c) = sum_a sigma(q,a), independent of c. A one-state CTMDP with actions c1 and c2 and rates 1 and 10 has no preimage. Proposition 5.17, which asserts the isomorphism without proof, cannot repair this—it would only relate CMAs to that smaller subclass.\n\nSecond, the expressiveness hierarchy, the paper's other headline, is not demonstrated. Theorems 3.29, 4.19, and 4.33 are proof sketches that largely restate classical inclusions; Proposition 3.23's proof sketch simply refers forward to Theorem 3.29. Proposition 3.31's sketch is okay in spirit but not rigorous, and Proposition 3.68 contains a concrete error: emptiness for nondeterministic Büchi automata is NLOGSPACE-complete, not PSPACE-complete.\n\nWhat is genuinely good: the layered definitions—controlled automata, probabilistic, then stochastic—are coherent and worth having. The policy taxonomy (memoryless, finite-memory, stack, tape) is natural. The SAN-to-automaton encoding for Theorem 3.13 has a full proof in Appendix A and is credible, even if it is a known-style Petri-net/Turing-machine simulation. The bisimulation equivalences are routine but correctly laid out.\n\nSo the paper is a serious attempt at a useful framework, but the load-bearing results are not in place. It reads like an extended abstract with the technical core promised in appendix to come. The author has real background in SANs; the self-citations are appropriate background.\n\nWho gets value: someone tracking SAN semantics or wanting a map of policy expressiveness would find this a useful progress report, not a finished foundation.\n\nFor peer review: yes, send it out—it is substantial enough that a good referee would catch the CTMDP issue and the missing proofs, and the author would benefit. But the editor should not expect acceptance; this is a major revision or reject.","headline":"The CTMDP generalization fails as stated because Definition 5.16 makes exit rates control-independent, and the expressiveness hierarchy is mostly proof sketches.","tokens_in":46521,"tokens_out":3472,"would_cite":false,"duration_ms":30701,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["68Q45","68Q60","93C65"],"pacs":[],"model":"deepseek-v4-flash","headline":"Controlled Stochastic Activity Networks unify nondeterministic, probabilistic, and stochastic behavior with explicit control policies, and subsume continuous-time Markov decision processes in the exponential case.","keywords":["controlled stochastic activity networks","control policies","automata-theoretic semantics","continuous-time Markov decision processes","probabilistic automata","language hierarchies","bisimulation","formal verification"],"falsifier":"Take a Controlled Markovian Automaton with two timed activities that have very different rates (say σ(q,a1)=1 and σ(q,a2)=100) and non-identical successor distributions for the same control action, construct the CTMDP from Definition 5.16, and compare finite-horizon state-distribution probabilities under every memoryless policy in both models. Any discrepancy would disprove Proposition 5.17 and collapse the claimed CTMDP generalization.","tokens_in":1543,"feed_emoji":"","tokens_out":2494,"duration_ms":81054,"temperature":0.7,"pith_summary":"The paper claims that extending Stochastic Activity Networks with explicit control actions yields a single semantic framework for nondeterministic, probabilistic, and stochastic system dynamics alongside policy-driven decision making. It builds a hierarchy of control policies—memoryless, finite-memory, stack-augmented, tape-augmented, and history-dependent—and shows that the languages they accept form a strict chain from regular to recursively enumerable languages, with computable history-dependent policies collapsing to tape-augmented ones. It also asserts that any computable controlled automaton can be realized by a computable controlled activity network, and that in the exponential-timing case the framework reduces to continuous-time Markov decision processes. If correct, this gives safety-critical system designers one compositional formalism in which control, timing, probability, and nondeterminism can be specified and analyzed together, reusing CTMDP verification techniques as a special case.","feed_headline":"Policy hierarchy spans regular to Turing-powerful control","feed_subtitle":"One framework unifies control, timing, and chance, with CTMDPs as a special case.","key_machinery":"The central object is the controlled automaton (Q, A, C, →, Q0), a state-transition system whose transitions are labeled by activities and control actions, together with policies that map histories to control actions. The expressiveness results are carried by augmenting this automaton with memory structures—finite-state memory, a stack, or a tape—so that each policy class becomes a language class. On the stochastic side, the key reduction is the Controlled Markovian Automaton, a compact representation with activity rate function σ(q,a) = ρ(q,a)α(q,a), and the CTMDP constructed in Definition 5.16 by aggregating rates and probabilities over activities for each control action. The modeling-powe","core_discovery":"The paper's central claim is that adding a finite set of control actions to Stochastic Activity Networks produces a layered family of automata—controlled automata, controlled probabilistic automata, and controlled stochastic automata—whose behavior is governed by policies selecting control actions at activity completions. Its main theorems assert that every computable controlled automaton is isomorphic to the automaton realized by some computable controlled activity network (Theorem 3.13); that the language classes induced by policy types satisfy the strict hierarchy L0 ⊂ LF ⊂ LStack ⊂ LTape = Lcomp_H ⊂ LH (Theorem 3.29), with global unions equal to REG, CFL, and RE; and that a Controlled Ma","pith_inferences":["The unproved Proposition 5.17 is the hinge of the CTMDP subsumption claim: until the state-process isomorphism between Controlled Markovian Automata and the constructed CTMDP is proved, the relationship to CTMDPs is an assertion rather than an established theorem.","The hierarchy's strictness is witnessed by classical separating languages interpreted as degenerate probabilistic systems; in genuinely stochastic settings with threshold semantics, those separations may blur, and the paper does not analyze threshold-sensitive collapses.","The modeling-power theorem establishes Turing-level expressiveness only through inhibitor gates and large auxiliary subnetworks, suggesting that practical analysis will need to restrict attention to sublanguages that remain algorithmically tractable.","If the CTMDP representation is made rigorous, the framework could inherit existing finite-state CTMDP solvers and PAC reinforcement-learning guarantees, but the precise passage from the paper's reward semantics to CTMDP optimal policies requires a fuller argument than the current unproved isomorphism provides."],"forward_implications":["Emptiness for controlled automata is decidable in polynomial time for memoryless and finite-memory policies, decidable for stack-augmented policies, and undecidable for tape-augmented or arbitrary history-dependent policies.","For controlled Büchi automata over infinite words, the same policy hierarchy persists, and emptiness is PSPACE-complete for memoryless and finite-memory policies and undecidable for richer policy classes.","For controlled probabilistic automata, threshold-based language emptiness is undecidable under history-dependent policies even when the plant is finite, so the probabilistic setting is strictly harder than the nondeterministic one.","Finite-state CTMDPs induced by Controlled SANs admit memoryless deterministic optimal policies for expected-total and discounted reward in polynomial time, while time-bounded reachability and reward objectives are PSPACE-complete.","For controlled stochastic automata with arbitrary timing distributions, discretized semi-Markov decision processes yield ε-optimal policies via contracting value iteration that converges geometrically."],"fun_headline_variants":["Policy hierarchy in controlled SANs spans regular to Turing-powerful","Controlled SANs unify nondeterminism, probability, and stochastic timing","From memoryless to Turing-powerful policies in one automata framework","Controlled SANs generalize CTMDPs with a strict language hierarchy","New framework combines control, timing, and chance with policy tiers"],"cache_read_input_tokens":47872,"weakest_assumption_plain":"The load-bearing premise is Proposition 5.17, which asserts without proof that the state process of a Controlled Markovian Automaton is isomorphic to the state process of the CTMDP built in Definition 5.16; if that isomorphism fails—due to the required normalization Σ_{q'} P(q,a,c,q') = 1 or to a mismatch in how control actions are selected after activity completions—the paper's headline claim that Controlled SANs generalize CTMDPs is not established.","fun_headline_variants_meta":{"raw":{"variants":["Policy hierarchy in controlled SANs spans regular to Turing-powerful","Controlled SANs unify nondeterminism, probability, and stochastic timing","From memoryless to Turing-powerful policies in one automata framework","Controlled SANs generalize CTMDPs with a strict language hierarchy","New framework combines control, timing, and chance with policy tiers"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000382,"raw_usage":{"total_tokens":1848,"prompt_tokens":718,"completion_tokens":1130,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":462,"completion_tokens_details":{"reasoning_tokens":1037}},"tokens_in":462,"tokens_out":1130,"duration_ms":9482,"temperature":1.0,"reasoning_tokens":1037,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T21:56:16.891715+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a Controlled Markovian Automaton with two timed activities that have very different rates (say σ(q,a1)=1 and σ(q,a2)=100) and non-identical successor distributions for the same control action, construct the CTMDP from Definition 5.16, and compare finite-horizon state-distribution probabilities under every memoryless policy in both models. Any discrepancy would disprove Proposition 5.17 and collapse the claimed CTMDP generalization.","supporting_citations":[],"review_version":1}