Temporal Trace Evaluation (TTE)

• Temporal Trace Evaluation (TTE) is a benchmark task that assesses LLMs' ability to simulate and analyze step-by-step transitions in formal, multi-state temporal systems.
• It employs automata derived from temporal logic specifications (e.g., LTL) to generate controlled trace sequences for rigorous diagnostic evaluation.
• Key metrics like per-step accuracy and F1 score reveal LLMs’ strengths in state tracking as well as their limitations handling complex, long-range dependencies.

Temporal Trace Evaluation (TTE) is a benchmark and evaluation task specifically designed to assess the capacity of reasoning systems—primarily LLMs—to simulate, interpret, and analyze the concrete, step-by-step execution of temporal, multi-state systems. Within the structured benchmark TempoBench, TTE focuses on the diagnostic deconstruction of "chain-based" or agentic reasoning systems, isolating the requirements for precise temporal state-tracking, logical consistency, and alignment with formally specified models of computation or control (e.g., finite-state machines derived from LTL specifications) (Holzer et al., 31 Oct 2025).

1. Conceptual Foundations and Formal Definition

Temporal Trace Evaluation centers around the notion of a "trace": a finite sequence of system states generated by a formal automaton (such as a Mealy machine), with each step corresponding to a specific mapping from input atomic propositions (APs) to output APs as determined by the automaton's transition function. The underlying system $A = (Q, E, \delta, q_0, F)$ transitions across state space $Q$ according to input $E$, transition function $\delta$, and outputs $F$.

The TTE task presents the LLM with an automaton and a concrete initial state, then asks for the correct sequence of state transitions or outputs given a sequence of input events. This requires the model to simulate the actual evolution of the system over time, step by step, ensuring adherence to the formal system definition.

2. Task Construction and Workflow

In the TempoBench framework, TTE problems are constructed as follows:

• System Synthesis: Temporal logic specifications (e.g., LTL) are compiled via tools such as LTLsynt and Spot to generate explicit finite-state automata (HOA format) representing realistic, reactive agents (e.g., controllers for arbiters, music players).
• Trace Sampling: The HOAX tool is used to produce valid traces (sequences of input/output pairs) reflecting possible system behaviors from initial states.
• Prompt Generation: Each TTE instance is framed in natural language, sometimes providing a tabular or semi-formal description of the initial state, the trace prefix, and requesting either the next step or the entire output trace for a given input sequence.

The model's task is not merely to predict the next or final output, but to faithfully follow the system's formal rules over multiple steps, capturing both the correct ordering and the right state transitions at each point.

3. Dimensions of Reasoning Evaluated

TTE distinguishes itself from general sequence prediction or unconstrained "reasoning" by requiring strict:

• Stateful Consistency: Models must maintain an internal memory of the automaton's state; simply remembering the last output is insufficient.
• Local and Global Consistency: Each step must follow deterministically from the prior state and input; errors at any point propagate, revealing sustained misunderstandings.
• Trace Algebra: The required outputs often follow from non-trivial rules embedded in the system (e.g., multi-step dependencies, toggling of outputs based on internal flags, guards, or history).

These requirements compel models to implement an implicit "interpreter" for the automaton, generalizing beyond table lookups or shallow rote memorization.

4. Evaluation Protocol and Metrics

The principal evaluation metrics for TTE in TempoBench are:

• Step-wise Accuracy: For each time step, the predicted output (or state) is compared to the ground truth. Full credit is given only for perfect agreement.
• F1 Score (per-step and aggregate): Measures overlap between predicted and actual output APs per step, rewarding partially correct answers.
• Trace-level Consistency: Sequence-wide metrics inspect whether the model sustains correctness over long horizons, penalizing "off-by-one" or cascading errors.

These metrics are designed to penalize both local confusion and global inconsistency, providing a high-resolution tool to diagnose reasoning errors.

5. Empirical Findings and LLM Capabilities

Experimental results from TempoBench indicate that state-of-the-art LLMs achieve moderately high performance on TTE:

Difficulty Setting	Per-step F1	Trace-level Accuracy
TTE-normal	up to 69.5%	Above 60%
TTE-hard	Moderate degradation; still >50%

Contrastingly, models' performance in TTE remains significantly higher than in temporal causal evaluation (TCE), especially as system complexity increases. Models track and reproduce step-by-step transitions reliably, even in longer or denser automata. This suggests LLMs have acquired an emergent capacity for simulating formal state-machines, likely via pretraining on program-like or decision-process data.

Further analysis demonstrates:

• Performance strongly correlates with trace complexity, length, and system state cardinality.
• Errors cluster around ambiguous or under-specified transitions but are rare when the system exhibits simple, deterministic behavior.
• The main failure mode is an inability to manage intricate, long-range dependencies or to "recover" from an error at a prior step, leading to divergence for the remainder of the trace.

6. Significance for Temporal Reasoning Research

TTE provides a diagnostic benchmark that separates low-level temporal simulation competence from higher-order causal reasoning:

• LLMs’ upper performance bound on TTE sets a baseline for interpreting results on more challenging temporal causal tasks.
• The TTE task exposes models' limitations in memory, internal simulation, and systematicity, but also reveals areas of successful grounding in formal system behavior.
• The divergence between TTE and TCE results in TempoBench emphasizes that temporal simulation is a necessary but not sufficient precondition for counterfactual causal inference or credit assignment.

The design of TTE aligns with demands in software agents, code assistants, or business process modeling, where accurate multi-step reasoning about stateful, reactive systems is essential.

7. Summary Table: Comparison of TTE and TCE in TempoBench

Aspect	Temporal Trace Evaluation (TTE)	Temporal Causal Evaluation (TCE)
Task focus	Simulate system trace (forward execution)	Identify cause-effect in traces
Formal grounding	Finite-state automata, LTL specifications	ω-regular causality, minimal causes
Measured ability	State tracking, step-wise consistency	Multi-step credit assignment, minimality
LLM performance	High (up to 69.5% F1)	Poor to moderate (7.5%–65.6% F1)
Bottleneck	Memory, propagation of early errors	Deep causal abstraction, counterfactuals

8. Implications, Limitations, and Future Directions

TTE as implemented in TempoBench exposes both the strengths and boundaries of current LLMs in temporally structured, symbolic reasoning. While contemporary models generalize well to trace-following tasks, failures on the more abstract causal tasks (TCE) highlight unsolved challenges in compositionality, generalization, and the integration of temporal symbolic reasoning with deeper causal inference. Ongoing research may focus on augmenting LLMs with structured system representations, stepwise planning, or explicit credit assignment modules to bridge the remaining gaps.

The TTE methodology, by generating parametrically controlled, verifiable, and realistic agentic reasoning tasks, provides a foundation for the systematic deconstruction and enhancement of model reasoning in temporal and agent-based domains (Holzer et al., 31 Oct 2025).